Question

If the speed of a moving particle is decreased by 1%, the de Broglie wavelength of the wave associated with it

• A. decreases by 1%
• B. increases by 1%
• C. decreases by 2%
• D. increases by 2%
• E. decreases by 5%

Hint:

Remember that the de Broglie wavelength is inversely proportional to the velocity, so any decrease in speed results in an increase in wavelength.

Answer 1

The Correct Option is B

Step 1: The de Broglie wavelength \(\lambda\) of a particle is given by \(\lambda = \frac{h}{mv}\), where \(h\) is Planck's constant, \(m\) is the mass, and \(v\) is the velocity of the particle. 
Step 2: A decrease in speed by 1% implies \(v' = 0.99v\). 
Step 3: The new wavelength \(\lambda'\) becomes \(\lambda' = \frac{h}{m \cdot 0.99v} = \frac{1}{0.99} \lambda \approx 1.01 \lambda\). 
Step 4: Thus, the de Broglie wavelength increases by approximately 1%.