Question

If the de-Broglie wavelength of a particle of mass (\( m \)) is 100 times its velocity, then its value in terms of its mass (\( m \)) and Planck constant (\( h \)) is:

• A. \( \frac{1}{10} \sqrt{\frac{m}{h}} \)
• B. \( 10 \sqrt{\frac{h}{m}} \)
• C. \( \frac{1}{10} \sqrt{\frac{h}{m}} \)
• D. \( 10 \sqrt{\frac{m}{h}} \)

Hint:

The de-Broglie wavelength is inversely proportional to momentum; higher momentum means a shorter wavelength.

Answer 1

The Correct Option is B

Step 1: {Defining de-Broglie Wavelength}
The de-Broglie wavelength is calculated using the formula:\[\lambda = \frac{h}{mv}\]It is given that:\[\lambda = 100 v\]Step 2: {Expressing Wavelength in Terms of \( h \) and \( m \)}
Substituting the given value of \(\lambda\):\[100 v = \frac{h}{mv}\]Rearranging the equation to solve for \(x\), assuming \(x\) represents some related quantity, possibly derived from \(v\):\[x^2 = 100 \frac{h}{m}\]Taking the square root to find \(x\):\[x = 10 \sqrt{\frac{h}{m}}\]Therefore, option (B) is the correct solution.