Question 9:
Figure 1 shows a photocell constructed using semiconductor material that can be activated by a light with a maximum wavelength of 1 110 nm.
(a) What is the threshold frequency and work function of the semiconductor?
(b) Why does the semiconductor look opaque at room temperature?
Answer:
(a)
$$ \begin{aligned} f_0 & =\frac{c}{\lambda_0} \\ & =\frac{3.00 \times 10^8}{1110 \times 10^{-9}} \\ & =2.70 \times 10^{14} \mathrm{~Hz} \end{aligned} $$
$$ \begin{aligned} W & =h f_0 \\ & =\left(6.63 \times 10^{-34}\right)\left(2.70 \times 10^{14}\right) \\ & =1.79 \times 10^{-19} \mathrm{~J} \end{aligned} $$
(b)
Figure 1 shows a photocell constructed using semiconductor material that can be activated by a light with a maximum wavelength of 1 110 nm.
(a) What is the threshold frequency and work function of the semiconductor?
(b) Why does the semiconductor look opaque at room temperature?
Answer:
(a)
$$ \begin{aligned} f_0 & =\frac{c}{\lambda_0} \\ & =\frac{3.00 \times 10^8}{1110 \times 10^{-9}} \\ & =2.70 \times 10^{14} \mathrm{~Hz} \end{aligned} $$
$$ \begin{aligned} W & =h f_0 \\ & =\left(6.63 \times 10^{-34}\right)\left(2.70 \times 10^{14}\right) \\ & =1.79 \times 10^{-19} \mathrm{~J} \end{aligned} $$
(b)
At room temperature, the thermal energy is insufficient to release electrons in a photocell or to activate the photocell.
Question 10:
Muthu conducted an experiment on a grain of sand falling through a small hole. Given the mass of the grain of sand is 5 × 10−10 kg, the diameter of the sand is 0.07 mm, the velocity of the sand falling through the hole is 0.4 m s−1 and the size of the hole is 1 mm:
(a) Estimate the de Broglie wavelength of the sand.
(b) Will the falling sand produce a diffraction pattern when passing through the small hole? Explain your answer.
Answer:
(a)
$$ \begin{aligned} \lambda & =\frac{h}{p} \\ & =\frac{h}{m v} \\ & =\frac{6.63 \times 10^{-34}}{\left(5 \times 10^{-10}\right)(0.4)} \\ & =3.32 \times 10^{-24} \mathrm{~m} \end{aligned} $$
(b)
No. The de Broglie wavelength of the sand is too short (10-24 m ) compared to the size of the hole ( 1 mm ). If the size of the hole is further reduced to approximate the order of the de Broglie wavelength, the sand will not be able to pass through it because the diameter of the sand is 0.07 mm.
Muthu conducted an experiment on a grain of sand falling through a small hole. Given the mass of the grain of sand is 5 × 10−10 kg, the diameter of the sand is 0.07 mm, the velocity of the sand falling through the hole is 0.4 m s−1 and the size of the hole is 1 mm:
(a) Estimate the de Broglie wavelength of the sand.
(b) Will the falling sand produce a diffraction pattern when passing through the small hole? Explain your answer.
Answer:
(a)
$$ \begin{aligned} \lambda & =\frac{h}{p} \\ & =\frac{h}{m v} \\ & =\frac{6.63 \times 10^{-34}}{\left(5 \times 10^{-10}\right)(0.4)} \\ & =3.32 \times 10^{-24} \mathrm{~m} \end{aligned} $$
(b)
No. The de Broglie wavelength of the sand is too short (10-24 m ) compared to the size of the hole ( 1 mm ). If the size of the hole is further reduced to approximate the order of the de Broglie wavelength, the sand will not be able to pass through it because the diameter of the sand is 0.07 mm.