Question

Light of two different frequencies whose photons have energies 1 eV and 2.5 eV, respectively, successively illuminate a metal whose work function is 0.5 eV. The ratio of the maximum speed of the emitted electrons will be:

• A. 1:2
• B. 1:1
• C. 1:3
• D. 1:4

Hint:

The speed of emitted electrons is proportional to the square root of their kinetic energy.

Answer 1

The Correct Option is C

Step 1: Use the photoelectric equation.
The maximum kinetic energy of the emitted electrons is given by: \[ K.E. = h \nu - \phi \] The speed of the emitted electrons is related to the kinetic energy.
Step 2: Calculation of speed ratio.
The ratio of the maximum speeds is proportional to the square root of the kinetic energy. The ratio of the speeds is therefore \( 1:3 \).
Final Answer: \[ \boxed{1:3} \]