Question

A photosensitive metallic surface has work function, hv₀. If photons of energy 2hv₀ fall on this surface, the electrons come out with a maximum velocity of 4x10⁶ m/s. When the photon energy is increased to 5hv₀, then maximum velocity of photoelectrons will be:

• A. 16x10⁶ m/s
• B. 8x10⁷ m/s
• C. 4x10⁵ m/s
• D. 8x10⁶ m/s

Answer 1

The Correct Option is D

When photons of frequency 2v₀ are incident, the Einstein equation is \(\frac{mv^2_1}{2}\) 
=\(2hv_0-hv_0\) or \(\frac{mv^2_1}{2}\) = \(hv_0\) ……(1). 
When photons of frequency \(5_{vo}\)are incident, the Einstein equation changes to \(\frac{mV^2_2}{2}\) = \(5hv_0-hv_0\) = \(4hv_0\)    .......(2)
Equation-2 is divided by Equation-1,  gave us \(v^2_2\) = \(4v^2_1\) or \(v_2\) =\(2v_1\) = 2 \(\times\) 4 \(\times\) 10⁶ m/s =8 \(\times\)10⁶ m/s.

Therefore, the correct option is (D): 8x10⁶ m/s