Question

Energy of the incident photon on the metal surface is \(3W\) and then \(5W\), where \(W\) is the work function of that metal. The ratio of velocities of emitted photoelectrons is

• A. \(1:4\)
• B. \(1:2\)
• C. \(1:\sqrt{2}\)
• D. \(1:1\)

Hint:

Find the kinetic energy of the electrons in each case using Einstein's equation, then use v proportional to the square root of K.

Answer 1

The Correct Option is C

Step 1: Speed in Terms of Energy
$v = \sqrt{\dfrac{2(E-W)}{m}}$, so $v \propto \sqrt{E-W}$.

Step 2: Substitute
$v_1 : v_2 = \sqrt{2W} : \sqrt{4W}$

Step 3: Simplify and Compare
$\sqrt{2} : 2 = 1 : \sqrt{2}$, which matches option (C).

Final Answer:
The speeds are in proportion to the square roots of 2W and 4W, which is 1 to root 2. \[ \boxed{\text{(C) }1:\sqrt{2}} \]