Answer to Question #87755 in Atomic and Nuclear Physics for Nicholas Legault

Question

Sodium has a work function of 2.36eV. If a beam of monochromatic 442-nm light is incident upon a sample of sodium, will electrons be ejected? At what speed?

Answer 1

1.

$$f_0=\frac{\phi}{h}=\frac{2.36eV}{4.135(10)^{-15}eVs}=5.71 \cdot 10^{14} Hz.$$

$$f = \dfrac{c}{\lambda} = \dfrac{3 \cdot 10^{8} \dfrac{m}{s}}{442 \cdot 10^{-9} m} = 6.78 \cdot 10^{14} Hz.$$

Since,

$$f>f_0$$

the electrons will be ejected from the surface of the sodium.

2.

$$0.5mv^2=hf - \phi = hf - hf_0 = h(f - f_0)$$

$$v = \sqrt{\dfrac{2h(f - f_0)}{m}}$$

$$v = \sqrt{\dfrac{2 \cdot 6.626 \cdot 10^{-34} \cdot ( 6.78 \cdot 10^{14} - 5.71 \cdot 10^{14} )}{9.1 \cdot 10^{-31} }} = 3.95 \cdot 10^5 \dfrac{m}{s}.$$