Question

An electron is travelling with a velocity \( v \) in free space and when it enters a medium, its velocity is reduced by 20%. The de Broglie wavelength of electron in the medium is \( \alpha\lambda_o \), where \( \lambda_o \) is its de Broglie wavelength in free space. The value of \( \alpha \) is \dots

• A. 1.20
• B. 1.0
• C. 1.25
• D. 0.75

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The de Broglie wavelength of a moving particle is inversely proportional to its momentum. Since the mass of the electron remains constant, the wavelength is inversely proportional to its velocity.
: Key Formula or Approach:
\( \lambda = \frac{h}{p} = \frac{h}{mv} \implies \lambda \propto \frac{1}{v} \).
Step 2: Detailed Explanation:
In free space, wavelength \( \lambda_o = \frac{h}{mv} \).
In the medium, velocity \( v' \) is reduced by 20%:
\[ v' = v - 0.20v = 0.80v = \frac{4}{5}v \].
The de Broglie wavelength in the medium is:
\[ \lambda_m = \frac{h}{mv'} = \frac{h}{m(0.8v)} = \frac{\lambda_o}{0.8} \]
\[ \lambda_m = \frac{10}{8} \lambda_o = 1.25 \lambda_o \].
Comparing with \( \lambda_m = \alpha \lambda_o \), we get \( \alpha = 1.25 \).
Step 3: Final Answer:
The value of \( \alpha \) is 1.25.