The energy that should be added to an electron to reduce its de - broglie wavelength from 1 nm to 0.5 nm is

Options

A. four times that initial energy
B. equal to the initial energy
C. two times the initial energy
D. three - times the initial energy

Answer

D

Explanation

Answer (4) `lambda = h/sqrt(2mE)
Rightarrow lambda alpha 1/sqrtE .
lambda_1/lambda_2 = sqrt(E_2/E_1 .
1/0.5 = sqrt(E_2/E_1).
Rightarrow E_2/E_1 = 4 .
therefore E_2 = 4E_1` .
The energy to be added = `E_2 - E_1 .
= 4E_1 - E_1 = 3E_1`