Question #87755
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?
1
Expert's answer
2019-04-10T09:43:52-0400

1.


f0=ϕh=2.36eV4.135(10)15eVs=5.711014Hz.f_0=\frac{\phi}{h}=\frac{2.36eV}{4.135(10)^{-15}eVs}=5.71 \cdot 10^{14} Hz.

f=cλ=3108ms442109m=6.781014Hz.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>f0f>f_0

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

2.


0.5mv2=hfϕ=hfhf0=h(ff0)0.5mv^2=hf - \phi = hf - hf_0 = h(f - f_0)

v=2h(ff0)mv = \sqrt{\dfrac{2h(f - f_0)}{m}}

v=26.6261034(6.7810145.711014)9.11031=3.95105ms.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}.


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