108年 - 國立台南一中教師甄選物理科#76763

1. In physics, the Planck length is a unit of length. It is developed by physicist Max Planck. The Planck length can be defined from three fundamental physical constants: the speed of light in vacuum c, the Planck constant h, and the gravitational constant G. Please use the dimensional analysis to derive the Planck length from c, h, and G.

2. Water is moving with a speed of 4 m/s through a pipe with a cross-sectional area of 5 cm². The water gradually descend 10 m as the pipe increases in area to 10 cm². If the pressure at the upper level is 1.5 x10⁵ Pa, what is the pressure at the lower level? (g=10 m/s²)

3. The temperature of 2.00 mol of hydrogen gas is raised 40.0 K at constant volume. The molecules in the gas rotate but do not oscillate. How much energy is transferred to the gas as heat Q?

4. Two waves are generated on a string of length 3.0 m to produce a three-loop standing wave with an amplitude of 1.0 cm. The wave speed is 100 m/s. Let the equation for one of the waves be of the form y(x,t) = y_m sin(kx + ωt). In the equation for the other wave, what are (1) k, and (2) ω?

5. An ambulance with a siren emitting a whine at 1710 Hz overtakes and passes a cyclist pedaling a bike at 10 m/s. After being passed, the cyclist hears a frequency of 1575 Hz. How fast is the ambulance moving? (the speed of sound in air is 340 m/s)

6. A thin flake of mica(n = 1.58) is used to cover one slit of a double-slit arrangement. The central point on the screen is occupied by what used to be the seventh bright fringe. If A = 6380 Å(in vacuum), what is the thickness of the mica?

7. The electric field in a region of space has the components E_y = E_z = Q and E_x = 4.00x (N/C). Point A is on thej; axis at y = 3.00 m, and point B is on the x axis at x = 4.00 m. What is the potential difference V_B - V_A?

8. Three charges of +0.1 C each are placed on the corners of an equilateral triangle, 1.0 m on a side. If energy is supplied at the rate of 1.0 KW, how many hours would be required to move one of the charges onto the midpoint of the line joining the other two?

9. Figure 1 shows a wood cylinder of mass m = 0.25 kg and length L =0.10 m, with N = 10 turns of wire wrapped around it longitudinally, so that the plane of the wire coil contains the long central axis of the cylinder. The cylinder is released on a plane inclined at an angle 6 to the horizontal, with the plane of the coil parallel to the incline plane. If there is a vertical uniform magnetic field of magnitude B = 0.50 T, what is the least current I through the coil that keeps the cylinder from rolling down the plane?

10. A stationary, circular wall clock has a face with a radius of 20 cm. Six turns of wire are wound around its perimeter; the wire carries a current 2.0 Ain the clockwise sense. The clock is located where there is a constant, uniform external magnetic field of 50 mT(but the clock still keeps perfect time). At exactly 1:00 p.m., the hour hand of the clock points in the direction of the external magnetic field. After how many minutes will the minute hand point in the direction of the torque on the winding due to the magnetic field?

11. Atom 1 of mass m\ and atom 2 of mass nn are both singly ionized with a charge of +q. After being introduced into a mass spectrometer and accelerated from rest through a potential difference V, each ion follows a semicircular path in a uniform magnetic field of magnitude B. What is the distance Ax between the points where the ions strike the detector?

12. One hundred turns of (insulated) copper wire are wrapped around a wooden cylindrical core of cross-sectional area 1.20x10^-3 m². The two ends of the wire are connected to a resistor. The total resistance in the circuit is 12.0 . If an externally applied uniform longitudinal magnetic field in the core changes from 1.60 T in one direction to 1.60 T in the opposite direction, how much charge flows through a point in the circuit during the change?

13. A pendulum consisting of a 0.01 kg mass is suspended from a string 0.1 m in length. Let the amplitude of its oscillation be such that the string in its extreme positions makes an angle of 11°(cosll° = 0.98) with the vertical. If its energy is quantized, what is the quantum number n (to the nearest order of magnitude)? (g = 10 m/s²) (According to this result, the quantized nature of the energy of the oscillations will not be apparent for large-scale system )

14. In a photoelectric experiment in which a sodium surface is used, one finds the maximum kinetic energy of photoelectrons is 0.62 eV for a wavelength of 4000 人，find the cutoff wavelength for sodium?

15. Consider an electron confined by electrical forces to move between two rigid “walls” separated by 1.5 A. What is the quantized energy value for the lowest stationary state?

二、問答計算題(共70分）

1.在推導氣體動力論巨觀現象與微觀行為關係式時，我們常用正立方體密閉容器當例子。若有學生詢問其他形狀密閉容器是否適用相同關係式，你會如何回答並舉例推導說明？（5%)

2.在推導單狹縫繞射關係式時，若有學生將狹缝視為無窮多點光源，並假設狹縫兩端點光源到光屏上P點之光程差為2λ，之後將狹縫分成等大小的A、B兩區，因這兩區的點光源皆對應相差1λ的光程差，為相長干涉。故學生推論光屏上P點為亮紋，請問你會如何更正該學生的錯誤？（5%)

3.如右圖，在平面平行板上坐標x = 0的 A點，有一束窄光垂直射到板上，板材料的折射率按公式變化，式中n₀和R為定值。光束在B點與原方向成（X角離開平行板，試求B點的 x 坐標？ (5%)

4.如右圖所示，厚度s、半徑R、質I m的金屬圓板，在平行地面之均勻磁場5中落下，若金屬圓板維持鉛直下落，使圓板面平行磁極且垂直地面，假設比R小很多，重力加速度以g表示。試求金屬圓板下落的加速度？（5%)

(1)請解出M給m之作用力？(5%)

(2)請用另一種方法解出M給m之作用力？(5%)

(3)請用200字以内說明這兩種方法在原理上(或是方法上)的差異？（5%)

6.在108課綱中自然領綱有關於「探究與實作」中敘寫著： .•…自然科學探究與實作的内容採不分科為原則。透過適當提問的主題探討和實作活動，引導學生體驗科學實踐的歷程。…「探究學習內容」著重於科學探究歷程，可歸納為四個主要項目：發現問題、規劃與研究、論證與建模、表達與分享。…「實作學習內容」為可實際進行操作的科學活動，例如：觀察、測量、資料蒐集與分析、歸納與解釋、論證與作結論等。.....

下表為探究學習内容的簡表

請依據領綱規定設計一個探究活動的課程計畫書，時間為4-6週（每週兩個小時）

♦注意事項：

(a)請在「單元/主題」攔位中敘寫活動主題名稱以及對應「探究學習内容」四個項目中哪一個項目

(b)請在「内容綱要」攔位中敘寫教師針對該主題在該週是如何進行實作活動

(c)本題評分原則是依據撰寫内容是否有依照領綱的相關規定(20%)

(1)請你選擇控制變因以及應變變因的單位，然後用200字以内說明您可以設計什麼樣實驗，其結果必須使用上表呈現。（答案不一定要是物理實驗。5%)

(2)在自然領綱中有關探究的學習内容，其中對於規劃與研究中「擬定研究計晝」有二條學習内容，其中一條是

•依據所提出的問題，計劃適當的方法、材料、設備與流程。

請用你(1)實驗設計說明、上表的資料數據、設計出一題四選一的單選題。其設計精神是為了測試學生在學習中是否有習得上述領綱的學習内容。（5%)

(3)在自然領綱中有關探究的學習内容，其中對於論證與建模中「解釋與推理」有三條學習内容，其中一條是

•由資料數據的變化趨勢，看出其蘊含的意義。

請用你(1)實驗設計說明、上表的資料數據、設計出一題四選一的單選題。其設計精神是為了測試學生在學習中是否有習得上述領綱的學習内容。（5%)

108年 - 國立台南一中教師甄選物理科#76763

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