Question

The light of wavelength $\lambda$ incident on the surface of metal having work function $\phi$ emits the electrons. The maximum velocity of emitted electrons is (c = velocity of light, m = mass of electron, h = Planck's constant)

• A. $\left[\frac{2(hc-\lambda\phi)}{m\lambda}\right]^{1/2}$
• B. $\left[\frac{2(h\nu-\lambda\phi)}{m\lambda}\right]^{1/2}$
• C. $\left[\frac{h\lambda-c\phi}{m\lambda}\right]^{1/2}$
• D. $\left[2\frac{h\phi-c\lambda}{m\lambda}\right]^{1/2}$

Answer 1

Answer: (A)

$\left[\frac{2(hc-\lambda\phi)}{m\lambda}\right]^{1/2}$

Answer 2

Energy balance: K.E. max = h c/λ − φ Velocity: v = √[2K.E./m] = √[(2(hc/λ − φ))/m] = √[(2(hc − φλ))/(mλ)]