AST_physics_test.jsonl

{"id": "AST physics - 110 - 2", "question": "假設在水波槽中, 與水波波速可能有關的物理量為重力加速度 $g$ 、水的密度 $\\rho$ 與水深 $D$ 。若僅以上述三個物理量的因次來判斷波速 $v$, 則下列何者正確?", "A": "$v$ 正比於 $\\rho g D$", "B": "$v$ 正比於 $g \\sqrt{\\rho D}$", "C": "$v$ 正比於 $\\frac{1}{\\sqrt{g D}}$", "D": "$v$ 正比於 $g D$", "E": "$v$ 正比於 $\\sqrt{g D}$", "F": null, "answer": "E", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.877269", "source": "AST physics - 110", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 110 - 3", "question": "假設棒球的旋轉與空氣阻力可被忽略, 回答第 3-4 題有關棒球的問題。\n某職棒投手先以固定力將靜止的棒球沿直線帶動約 $1.5 \\mathrm{~m}$ 的長度後, 投出 $144 \\mathrm{~km} / \\mathrm{h}$的快速直球。已知棒球的質量約為 $150 \\mathrm{~g}$, 則該投手施於球的固定力量值約為何?", "A": "$130 \\mathrm{~N}$", "B": "$80 \\mathrm{~N}$", "C": "$100 \\mathrm{~N}$", "D": "$120 \\mathrm{~N}$", "E": "$110 \\mathrm{~N}$", "F": null, "answer": "B", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.877278", "source": "AST physics - 110", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 110 - 4", "question": "假設棒球的旋轉與空氣阻力可被忽略, 回答第 3-4 題有關棒球的問題。\n棒球抵達本壘板上方時, 在離地 $1.0 \\mathrm{~m}$ 的高度, 被打擊者以與水平面夾角為 $\\theta\\left(\\cos \\theta=\\frac{3}{5}\\right)$ 的仰角、量值為 $126 \\mathrm{~km} / \\mathrm{h}$ 的速度反向擊出, 該球在被擊出後 $5.0 \\mathrm{~s}$ 恰好飛越全壘打牆的上空, 試問球飛越全壘打牆瞬間, 離地高度為多少 $\\mathrm{m}$ ? (假設棒球場地面為水平, 取重力加速度 $g=10 \\mathrm{~m} / \\mathrm{s}^{2}$ )", "A": "8", "B": "12", "C": "16", "D": "4", "E": "10", "F": null, "answer": "C", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.877286", "source": "AST physics - 110", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 110 - 11", "question": "科學家常用 $X$-射線繞射來測知晶體結構, 若將波長為 $\\lambda$ 的 $X$-射線改用電子束取代, 並進行相同晶體的繞射實驗, 以測得相同的繞射圖樣, 則電子的能量為何? ( $h$ 為普朗克常數, $m$ 為電子質量)", "A": "$\\frac{h^{2}}{2 m^{2} \\lambda^{2}}$", "B": "$\\frac{h^{2}}{2 m \\lambda^{2}}$", "C": "$\\frac{h^{2}}{m \\lambda^{2}}$", "D": "$\\frac{h}{2 m \\lambda}$", "E": "$\\frac{h^{2}}{m \\lambda}$", "F": null, "answer": "B", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.877293", "source": "AST physics - 110", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 110 - 15", "question": "地震預警是利用地震在地球內部傳播的 $\\mathrm{P}$ 波與 $\\mathrm{S}$ 波的速度差, 透過偵測首先到達的 $\\mathrm{P}$ 波來判斷地震規模, 在振動強烈的 $\\mathrm{S}$ 波到達前的時間內發出預警, 以利後續應變。回答第 $14-15$ 題。\n當地震表面波在稍後到達某地區時, 假設固定於地面的物體僅作水平方向的簡諧運動, 其振幅為 $0.20 \\mathrm{~cm}$, 週期為 $0.40 \\mathrm{~s}$, 最大加速度量值為 $a \\mathrm{~m} / \\mathrm{s}^{2}$ 。若固定於地面的水平書架上的書本不會因地震而滑動, 則書本與書架板間的靜摩擦係數不能小於 $\\mu$ 。以下各組 $(a, \\mu)$ 數值，何者正確？（取重力加速度 $g=10 \\mathrm{~m} / \\mathrm{s}^{2}$ )", "A": "$(1.0,0.10)$", "B": "$(0.50,0.10)$", "C": "$(0.25,0.050)$", "D": "$(0.50,0.050)$", "E": "$(1.5,0.15)$", "F": null, "answer": "D", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.877300", "source": "AST physics - 110", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 110 - 16", "question": "由許多個處於基態的氫原子所組成的系統, 吸收一束單一頻率的光後各自躍遷到主量子數為 $n$ 的激發態, 當這些處於激發態的氫原子回到基態時, 可以測量到六條不同波長的光譜線, 試問 $n$ 為何?", "A": "6", "B": "7", "C": "5", "D": "4", "E": "3", "F": null, "answer": "D", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.877308", "source": "AST physics - 110", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 110 - 18", "question": "臺東的臺灣國際熱氣球嘉年華是很受歡迎的休旅活動。要讓熱氣球升空, 必須加熱氣球裡的空氣, 使氣球體積變大, 以增加空氣浮力 (物體所受的空氣浮力等於物體在空氣中所排開同體積空氣的重量）。\n有一熱氣球乘載四人後的總質量為 $6.0 \\times 10^{2} \\mathrm{~kg}$ (不含球內空氣)。當加熱其內空氣, 使其體積膨脹至 $3.0 \\times 10^{3} \\mathrm{~m}^{3}$, 即可升空, 此時空氣浮力等於熱氣球載人後的總重量（含球內的空氣）, 則熱氣球內的空氣溫度是多少 ${ }^{\\circ} \\mathrm{C}$ ? (設當時外界氣溫為 $22^{\\circ} \\mathrm{C}$, 空氣密度為 $1.2 \\mathrm{~kg} / \\mathrm{m}^{3}$, 氣球內、外的空氣都視為理想氣體, 且加熱時球外空氣的溫度、壓力不變。)", "A": "81", "B": "72", "C": "57", "D": "42", "E": "22", "F": null, "answer": "A", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.877313", "source": "AST physics - 110", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 110 - 19", "question": "在核電廠發生重大核安事故後, 附近可檢測出放射性元素銫 -137 , 銫 -137 自發衰變時, 核子數減少至原來數目一半所需時間 (半衰期) 約為 30 年。已知每 1 公克銫 -137 的放射性活度約為 $3.2 \\times 10^{12} \\mathrm{~Bq}(\\mathrm{~Bq}$ 為放射性活度的單位, $1 \\mathrm{~Bq}=$ 每秒發生一次衰變; 活度亦稱活性) ; 食品中放射性銫檢驗的容許量標準值為 $100 \\mathrm{~Bq} / \\mathrm{kg}$ 。\n假設一尾 $100 \\mathrm{~kg}$ 的大型海魚在 15 年前體內的放射性物質只有 $2.0 \\times 10^{-8}$ 公克的放射性銫 - 137, 現今對其殘留的銫 -137 進行檢驗, 若銫 -137 在這期間未被代謝出體外, 則其每公斤的放射性活度為食品檢驗容許量之標準值的幾倍?", "A": "4.5", "B": "0.045", "C": "32", "D": "0.32", "E": "450", "F": null, "answer": "A", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.877318", "source": "AST physics - 110", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 111 - 1", "question": "下列何者等於 $1.0 \\mathrm{~N}$ 的力?", "A": "能使質量為 $1.0 \\mathrm{~g}$ 之物體的加速度為 $1.0 \\mathrm{~cm} / \\mathrm{s}^{2}$ 的力", "B": "能使質量為 $1.0 \\mathrm{~kg}$ 之物體的加速度為 $9.8 \\mathrm{~m} / \\mathrm{s}^{2}$ 的力", "C": "質量為 $1.0 \\mathrm{~kg}$ 之物體所受的重力", "D": "能使質量為 $1.0 \\mathrm{~kg}$ 之物體的加速度為 $1.0 \\mathrm{~m} / \\mathrm{s}^{2}$ 的力", "E": "質量為 $1.0 \\mathrm{~g}$ 之物體所受的重力", "F": null, "answer": "D", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.878534", "source": "AST physics - 111", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 111 - 6", "question": "一樂器上張緊的絃兩端固定, 其基音頻率 $f_{0}=252 \\mathrm{~Hz}$ 。若在張力不變下, 按住此絃的中點, 則彈奏此絃時發出基音 $f_{0}{ }^{\\prime}$ 為 $f_{0}$ 的多少倍?", "A": "4", "B": "2", "C": "0.5", "D": "0.25", "E": "1", "F": null, "answer": "B", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.878566", "source": "AST physics - 111", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 111 - 7", "question": "一容器內的理想氣體, 莫耳數為 $n$, 內能為 $U$, 密度為 $\\rho$, 壓力為 $P$, 絕對溫度為 $T$,氣體分子的方均根速率為 $v$, 理想氣體常數為 $R$ 。依據氣體動力論, 在熱平衡狀態下,下列關係何者正確?", "A": "$P=\\rho v^{2} / 2$", "B": "$P v=n R T$", "C": "$U=n R T$", "D": "$P=\\rho v^{2} / 3$", "E": "$U=3 P v / 2$", "F": null, "answer": "D", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.878573", "source": "AST physics - 111", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 111 - 8", "question": "有一項理論認為所有比鐵重的元素都是超新星爆炸時形成的。已知 ${ }^{235} \\mathrm{U}$ 和 ${ }^{238} \\mathrm{U}$ 的半衰期分別為 $0.704 \\times 10^{9}$ 年和 $4.47 \\times 10^{9}$ 年, 若地球上的鈾來自 $5.94 \\times 10^{9}$ 年前的恆星爆炸, 且爆炸時產生相同數量的 ${ }^{235} \\mathrm{U}$ 和 ${ }^{238} \\mathrm{U}$, 則目前地球上兩者的數量比 ${ }^{235} \\mathrm{U} /{ }^{238} \\mathrm{U}$ 約為下列何者?", "A": "$2^{-3}$", "B": "$2^{-9}$", "C": "$2^{-1}$", "D": "$2^{-5}$", "E": "$2^{-7}$", "F": null, "answer": "E", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.878578", "source": "AST physics - 111", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 111 - 9", "question": "下列哪一現象, 不能將光視為只是粒子或只是波, 而必須根據光具有二象性才能解釋?", "A": "一個氫原子躍遷發出的光向四周傳播時, 另一氫原子可吸收此光的全部能量", "B": "光由空氣中入射到金屬表面後會被反射", "C": "光沿著直線前進可穿過真空由太陽傳至地球", "D": "光在大氣中會折射而沿彎曲的路線前進, 產生海市蜃樓的現象", "E": "光通過狹縫後在遠處屏幕上可形成明暗相間的干涉條紋", "F": null, "answer": "A", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.878582", "source": "AST physics - 111", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109_補 - 1", "question": "下列有關物質波的敘述何者正確?", "A": "物質波的性質僅存在於不帶電的粒子; 例如, 中子是不帶電的粒子, 由中子照射晶體的實驗, 才能顯現物質波的性質", "B": "電子是帶電粒子, 電子束穿透金屬晶格的實驗中, 由於庫侖靜電力的作用, 雖然得到電子的繞射圖案, 但未必能證明電子具有波的性質", "C": "棒球以 150 公里/ 小時的速率運動, 其物質波的性質顯著且易於觀察", "D": "運動中的基本粒子不具有物質波的性質", "E": "以適當能量的單電子通過雙狹縫, 觀察雙狹縫後方屏幕, 每次電子在屏幕上留下一個亮點, 重複多次相同實驗, 在屏幕上累積留下的亮點可形成亮暗條紋", "F": null, "answer": "E", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.879870", "source": "AST physics - 109_補", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109_補 - 2", "question": "某生彈奏吉他時, 覺得吉他音調不準, 於是轉動吉他調音旋鈕, 將第二根弦稍微拉緊。若弦的兩固定端距離不變, 此調音動作對第二根弦產生的物理效應為何?", "A": "使第二根弦上駐波的頻率變大", "B": "使第二根弦上駐波和音箱的共鳴程度增大", "C": "使第二根弦上駐波的振幅變大", "D": "使第二根弦上駐波的波速變小", "E": "使第二根弦上駐波的波長變小", "F": null, "answer": "A", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.879889", "source": "AST physics - 109_補", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109_補 - 4", "question": "有一紅光雷射發射波長為 $6.3 \\times 10^{-7} \\mathrm{~m}$ 的雷射光, 其輸出功率為 $5.0 \\mathrm{~mW}$; 另有一藍光雷射發射波長為 $4.5 \\times 10^{-7} \\mathrm{~m}$ 的雷射光, 其輸出功率為 $15 \\mathrm{~mW}$ 。試問藍光雷射每秒發射的光子數目, 約為紅光雷射的多少倍?", "A": "3", "B": "4.2", "C": "0.47", "D": "0.24", "E": "2.1", "F": null, "answer": "E", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.879899", "source": "AST physics - 109_補", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109_補 - 5", "question": "一力常數為 $1.00 \\mathrm{~N} / \\mathrm{m}$ 的彈簧, 一端固定在牆上, 另一端連結質量為 $1.00 \\mathrm{~kg}$ 的質點, 且質點在光滑水平面上作一維簡諧運動, 以 $x$ 代表質點偏離平衡點（彈簧自然長度) 的位移, $x>0$ 表示彈簧被拉長, $x<0$ 表示彈簧被壓縮。在時間 $t=0 \\mathrm{~s}$時, 質點朝彈簧伸長的方向運動速率不為零, 且位移 $x=0.02 \\mathrm{~m}$ 。若運動過程中力學能守恆, 則時間 $t=\\pi \\mathrm{s}$ 時, 下列有關質點運動的敘述何者正確?", "A": "質點動量和時間 $t=0 \\mathrm{~s}$ 時的動量一樣", "B": "質點回到平衡點, 且開始被壓縮", "C": "質點回到平衡點, 且開始被拉長", "D": "朝彈簧壓縮的方向運動, 且 $x=0.02 \\mathrm{~m}$", "E": "朝彈簧壓縮的方向運動, 且 $x=-0.02 \\mathrm{~m}$", "F": null, "answer": "E", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.879905", "source": "AST physics - 109_補", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109_補 - 6", "question": "某生質量 $50.0 \\mathrm{~kg}$, 從一個 $10.0 \\mathrm{~m}$ 長的溜滑梯斜面滑下, 此斜面頂端與底部之間的垂直高度差為 $6.0 \\mathrm{~m}$ 。若該生下滑時所受的動摩擦力保持不變, 且溜滑梯斜面與該生間之動摩擦係數為 0.25 , 則該生沿斜面下滑的加速度量值為多少? ( 取重力加速度為 $10 \\mathrm{~m} / \\mathrm{s}^{2}$ )", "A": "$4.0 \\mathrm{~m} / \\mathrm{s}^{2}$", "B": "$8.0 \\mathrm{~m} / \\mathrm{s}^{2}$", "C": "$2.0 \\mathrm{~m} / \\mathrm{s}^{2}$", "D": "$6.0 \\mathrm{~m} / \\mathrm{s}^{2}$", "E": "$1.0 \\mathrm{~m} / \\mathrm{s}^{2}$", "F": null, "answer": "A", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.879911", "source": "AST physics - 109_補", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109_補 - 7", "question": "若低空運行的人造衛星, 其軌道半徑可視為地球半徑, 則該人造衛星的週期最接近下列何者? (取地球半徑 $R=6.4 \\times 10^{3} \\mathrm{~km}$ 、重力加速度 $g=10 \\mathrm{~m} / \\mathrm{s}^{2}$ )", "A": "$60 \\mathrm{~min}$", "B": "$84 \\mathrm{~min}$", "C": "$84 \\mathrm{~s}$", "D": "$6 \\mathrm{~min}$", "E": "$60 \\mathrm{~s}$", "F": null, "answer": "B", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.879916", "source": "AST physics - 109_補", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109_補 - 9", "question": "材質與半徑完全相同的兩金屬球分別帶有電量 $Q$ 及 $\\frac{1}{2} Q$, 兩球間的距離遠大於其半徑, 且兩球間的靜電作用力為 $F$ 。今將兩球接觸後再將它們放回原來位置, 假設過程中兩球上的總電荷守恆, 則兩球間的靜電作用力變為若干?", "A": "$\\frac{7}{8} F$", "B": "$\\frac{3}{2} F$", "C": "$\\frac{3}{4} F$", "D": "$\\frac{5}{4} F$", "E": "$\\frac{9}{8} F$", "F": null, "answer": "E", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.879925", "source": "AST physics - 109_補", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109_補 - 15", "question": "某生進行光電效應實驗, 使用的正極板與負極板表面均為金屬鈉, 其功函數為 $2.3 \\mathrm{eV}$, 而電源提供的電位差為 $3.0 \\mathrm{~V}$ 。通常在光電效應實驗中是將光照射在正極板上, 但某生在實驗中卻將波長 $400 \\mathrm{~nm}$ 的光照射在負極板上, 則光電子到達正極板時的最大動能約為何? (取普朗克常數 $h=6.63 \\times 10^{-34} \\mathrm{~J} \\cdot \\mathrm{s}$, 基本電荷 $e=1.6 \\times 10^{-19} \\mathrm{C}$, 光速 $c=3.0 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$ )", "A": "$0.8 \\mathrm{eV}$", "B": "$3.1 \\mathrm{eV}$", "C": "$5.4 \\mathrm{eV}$", "D": "$2.3 \\mathrm{eV}$", "E": "$3.8 \\mathrm{eV}$", "F": null, "answer": "E", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.879936", "source": "AST physics - 109_補", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109 - 1", "question": "新型冠狀病毒與流感病毒可使人類感染致病, 甚至危害生命, 因此必須防止病毒傳播。進出公共場所用額溫槍量測額溫、戴口罩及利用紫外線消滅病毒等都是可行的措施。回答第 1-2 題。\n新型冠狀病毒防疫期間, 常使用額溫槍量測人體額溫, 下列敘述何者正確?", "A": "額溫槍需與額頭表面皮膚達熱平衡才能準確量測額溫", "B": "額溫槍偵測到最大輻射強度的輻射頻率, 隨額溫升高而變小", "C": "額溫槍偵測的主要波段為紫外線範圍", "D": "額溫槍量測額溫的物理原理與偵測宇宙背景輻射類似", "E": "額溫槍偵測到主要波段的輻射強度越強, 表示額溫越低", "F": null, "answer": "D", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.881231", "source": "AST physics - 109", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109 - 2", "question": "新型冠狀病毒與流感病毒可使人類感染致病, 甚至危害生命, 因此必須防止病毒傳播。進出公共場所用額溫槍量測額溫、戴口罩及利用紫外線消滅病毒等都是可行的措施。回答第 1-2 題。\n表面沾有流感病毒的口罩, 可使用波長為 $253.7 \\mathrm{~nm}$ 的紫外線 $-\\mathrm{C}$ 照射, 破壞病毒的去氧核糖核酸（DNA）及核糖核酸（RNA）結構, 達到消滅病毒的效果。若以強度為 $6,600 \\mu \\mathrm{W} / \\mathrm{cm}^{2}$ 的紫外線 $-\\mathrm{C}$ 垂直照射口罩表面 $2.0 \\mathrm{~s}$, 則兩秒鐘內每平方公分的紫外線 $-\\mathrm{C}$ 光子數約為若干？(普朗克常數 $h=6.63 \\times 10^{-34} \\mathrm{~J} \\cdot \\mathrm{s}$, 光速 $c=3.0 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$ )", "A": "$1.7 \\times 10^{16}$", "B": "$9.6 \\times 10^{17}$", "C": "$2.4 \\times 10^{13}$", "D": "$8.4 \\times 10^{15}$", "E": "$6.4 \\times 10^{14}$", "F": null, "answer": "A", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.881254", "source": "AST physics - 109", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109 - 3", "question": "$\\mathrm{X}$ 射線應用於醫學影像及晶體結構分析, 其頻率範圍約在 $3 \\times 10^{17} \\mathrm{~Hz}$ 至 $3 \\times 10^{19} \\mathrm{~Hz}$ 。下列有關X射線的敘述何者正確? (光速 $c=3.0 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$ )", "A": "用狹縫間距為 $0.1 \\mathrm{~mm}$ 的雙狹縫即可觀察到 $X$ 射線的干涉條紋", "B": "X射線的路徑不受磁場與電場的影響", "C": "$X$ 射線可顯示晶體結構, 是由於其高穿透力特性所產生", "D": "X射線可顯示骨骼結構影像, 是由於波的干涉所產生", "E": "氫原子光譜的來曼系就有 X射線的頻率", "F": null, "answer": "B", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.881260", "source": "AST physics - 109", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109 - 4", "question": "一質點作週期運動, 經測量發現, 位移平方的平均等於 $X^{2}$, 動量平方的平均等於 $P^{2}$, 總力學能等於 $E$, 下列何者的因次與週期相同?", "A": "$X^{2} P^{2} / E$", "B": "$\\sqrt{X^{2} P^{2}} / E$", "C": "$E \\sqrt{X^{2} / P^{2}}$", "D": "$\\sqrt{X^{2} E^{2}} / P^{2}$", "E": "$E \\sqrt{P^{2} / X^{2}}$", "F": null, "answer": "B", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.881265", "source": "AST physics - 109", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109 - 10", "question": "一體積可變的密閉容器內裝有可視為理想氣體的定量氦氣, 當氣體的體積為 $V_{0}$ 、溫度為絕對溫度 $T_{0}$ 時, 氣體分子的方均根速率為 $v_{0}$ 。經由某一過程達到熱平衡後,氣體的體積變為 $V_{0} / 2$ 、溫度變為 $4 T_{0}$, 則此時氣體分子的方均根速率為何?", "A": "$8 v_{0}$", "B": "$2 v_{0}$", "C": "$v_{0} / 2$", "D": "$4 v_{0}$", "E": "$v_{0}$", "F": null, "answer": "B", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.881271", "source": "AST physics - 109", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109 - 11", "question": "進行「載流導線的磁效應」的示範實驗時, 將導線連接可變電阻及電源後, 卻沒有看到指北針的指針偏轉，下列使用三用電表檢修該實驗電路的方式，何者不正確?", "A": "三用電表和電路串聯, 以電流檔量測, 確定迴路上有電流通過", "B": "為測量導線電阻值, 先選擇三用電表的電阻檔, 再將兩支量測棒碰觸短路,作歸零校正", "C": "將導線連接電源後, 再以電阻檔量測導線電阻, 確定導線是否為斷路", "D": "三用電表測得電壓和電阻值, 計算電流的大小是否足夠使指針偏轉", "E": "三用電表和電源並聯, 以電壓檔量測, 確定電源有電壓輸出", "F": null, "answer": "C", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.881276", "source": "AST physics - 109", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109 - 13", "question": "有一雙狹縫裝置, 其狹縫間距為 $d$, 屏幕與雙狹縫平行、距離為 $L$, 以一束綠色雷射光經空氣垂直射入雙狹縫, 在屏幕上相鄰兩亮紋間距為 $x_{1}$ 。若改在平靜的水中進行上述實驗, 其餘條件皆相同, 在屏幕上相鄰兩亮紋間距為 $x_{2}$, 則 $x_{2} / x_{1}$ 之值為何? (已知水的折射率為 4/3)", "A": "$2 / 3$", "B": "$3 / 2$", "C": "1", "D": "$3 / 4$", "E": "$4 / 3$", "F": null, "answer": "D", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.881285", "source": "AST physics - 109", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109 - 15", "question": "長笛與單簧管為常見的管樂器, 長笛的管柱兩端皆為開口 單簧管的管柱一端封閉而另一端開口。吹奏時, 透過按壓管柱的音孔, 可改變管內空氣柱長度, 當吹氣通過簧片或管口產生聲音的頻率與空氣柱振動頻率相同時, 會發生共振並在管內空氣柱形成駐波。若忽略聲音駐波的管口修正量, 當長笛吹奏出基音的頻率與單簧管第一泛音的頻率相同時, 此時長笛空氣柱長度為單簧管空氣柱長度的幾倍?", "A": "$3 / 2$", "B": "$2 / 3$", "C": "$1 / 2$", "D": "$4 / 3$", "E": "$3 / 4$", "F": null, "answer": "B", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.881291", "source": "AST physics - 109", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109 - 16", "question": "已知氫原子的能階公式為 $E_{n}=-13.6 / n^{2} \\mathrm{eV}$, 其中 $n$ 為主量子數。一個動能為 $12.3 \\mathrm{eV}$的電子與基態的氫原子發生碰撞, 下列何者可能為激發後的襄原子所發出的光子能量 ?", "A": "$12.8 \\mathrm{eV}$", "B": "$0.7 \\mathrm{eV}$", "C": "$1.5 \\mathrm{eV}$", "D": "$1.9 \\mathrm{eV}$", "E": "$12.3 \\mathrm{eV}$", "F": null, "answer": "D", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.881296", "source": "AST physics - 109", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 109 - 20", "question": "蘇花公路山區改善路段 (簡稱蘇花改) 已全線通車, 包含隧道內的部分路段, 行車最高速限於 2020 年 6 月 20 日正式調整至 70 公里 / 小時。目前的科技, 可以在長隧道內每隔一段區間建置一個具有自動化設備的偵測點, 以兩固定點間之平均速率偵測是否超速。有一輛汽車駛入一長直隧道內, 隧道內某段區間的兩偵測點間距離為 4.2 公里, 該車之車尾通過第一個偵測點時的速率為 66 公里 / 小時,汽車以等加速運動行駛 36 秒後速率達到 74 公里/小時, 接著以等速率行駛 60 秒, 然後以等減速運動行駛。為使汽車在兩偵測點間之平均速率不超過最高速限 70 公里 / 小時, 該車之車尾通過第二個偵測點時的最高速率為何?", "A": "64 公里 / 小時", "B": "60 公里 / 小時", "C": "68 公里 / 小時", "D": "66 公里 / 小時", "E": "62 公里 / 小時", "F": null, "answer": "E", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.881302", "source": "AST physics - 109", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 112 - 1", "question": "下列選項的因次何者與能量因次不同?", "A": "質量乘以速率平方", "B": "力矩乘以角度", "C": "衝量乘以時間", "D": "壓力乘以體積", "E": "電量乘以電壓", "F": null, "answer": "C", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.882189", "source": "AST physics - 112", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 112 - 2", "question": "下列關於電磁波的敘述, 何者正確?", "A": "相同強度的電磁波頻率越高, 在真空中傳播的速率越快", "B": "可見光是電磁波, 在真空中與介質中均以相同速率傳播", "C": "電磁波與力學波一樣都有反射、折射、干涉與繞射現象", "D": "電磁波為縱波", "E": "只要電場和磁場同時存在, 便會產生交互作用而形成電磁波", "F": null, "answer": "C", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.882208", "source": "AST physics - 112", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 112 - 3", "question": "珠寶商使用最小刻度為 $1 \\mathrm{mg}$ 的電子科測量金飾質量 5 次, 求得平均值為 $m_{\\mathrm{AV}}$, 標準差為 $\\mathrm{SD}$ 。若以 $u_{\\mathrm{A}}$ 、 $u_{\\mathrm{B}}$ 與 $u_{\\mathrm{C}}$ 分別代表標準的 $\\mathrm{A}$ 類、 $\\mathrm{B}$ 類與組合不確定度, 且已知分析過程計算機顯示 $m_{\\mathrm{AV}}$ 為 $95.367823 \\mathrm{~g} 、 u_{\\mathrm{C}}$ 為 $0.35686524 \\mathrm{mg}$, 則下列選項何者正確? \\\\ \n", "A": "金飾質量的報告應為 $m_{\\mathrm{AV}}=95.36782 \\mathrm{~g}, u_{\\mathrm{C}}=0.36 \\mathrm{mg}$", "B": "$u_{\\mathrm{A}}=\\mathrm{SD} / 4$", "C": "$u_{\\mathrm{B}}=1 \\mathrm{mg}$", "D": "$u_{\\mathrm{C}}=\\left(u_{\\mathrm{A}}+u_{\\mathrm{B}}\\right) / 2$", "E": "金飾質量的報告應為 $m_{\\mathrm{AV}}=95.4 \\mathrm{~g}, u_{\\mathrm{C}}=0.4 \\mathrm{mg}$", "F": null, "answer": "A", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.882215", "source": "AST physics - 112", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 112 - 5", "question": "某生設計了一個不需使用計時器而可量測重力加速度的實驗。他選用了一個彈力常數為 $k$ 、自然長度為 $l$ 、繫有質量為 $m$ 之質點的彈簧, 使其作水平面之簡諧運動。再以一個擺長為 $L$ 、擺錘不計體積、質量為 $M$ 的單擺, 調整其擺長 $L$, 使兩個系統之簡諧運動的週期相同, 則其所測得的重力加速度量值為何?", "A": "$L k / m$", "B": "$l k / M$", "C": "$\\mathrm{Lm} / \\mathrm{k}$", "D": "$L M / k$", "E": "$l M / k$", "F": null, "answer": "A", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.882225", "source": "AST physics - 112", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 112 - 7", "question": "在光電效應實驗中, 若入射光頻率固定, 僅增加光的強度, 而其餘條件不變, 則增加的是下列光子的哪個物理量?", "A": "光子速度", "B": "單一光子的動量", "C": "單位時間入射的光子總數", "D": "單一光子的能量", "E": "光子質量", "F": null, "answer": "C", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.882230", "source": "AST physics - 112", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 112 - 12", "question": "1868 年法國天文學者發現來自太陽的光譜有幾道特殊的暗紋, 推斷是新元素的特性光譜,這個新元素就以太陽的希臘文命名為氦。已知太陽光譜會出現上述暗紋的原因, 是因為氦原子會吸收特定頻率的入射光子所造成的, 則下列敘述何者正確?", "A": "氦原子光譜的暗紋頻率和氫原子光譜的暗紋頻率完全相同", "B": "某元素光譜的暗紋頻率和氦原子光譜的暗紋頻率相同, 則此元素一定是氦", "C": "氦原子光譜的暗紋頻率和氛原子光譜的暗紋頻率完全相同", "D": "會出現暗紋是因為氦原子會將特定頻率光子繞射到不同的方向", "E": "會出現暗紋其實就是因為氦原子會被入射光游離", "F": null, "answer": "B", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.882236", "source": "AST physics - 112", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}
{"id": "AST physics - 112 - 13", "question": "甲、乙兩顆大小相同但質量不同的均匀小球, 自同一高度以不同的初速水平抛出, 落在平坦的地面上。已知甲球的質量為乙球的 4 倍, 但甲球的初速為乙球的一半。若不計空氣阻力, 則下列敘述何者錯誤?", "A": "乙球的水平射程較大", "B": "落地前瞬間, 兩球的加速度相等", "C": "落地前瞬間, 乙球的動能較大", "D": "落地前瞬間, 兩球速度的鉛直分量相等", "E": "兩球在空中的飛行時間相等", "F": null, "answer": "C", "explanation": "", "metadata": {"timestamp": "2023-10-16T22:05:11.882244", "source": "AST physics - 112", "explanation_source": ""}, "human_evaluation": {"quality": "", "comments": ""}}