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BITSAT 2024
Exam
BITSAT
Year
2024
Subject
Chemistry
Chapter
Structure of Atom

BITSAT 2024 · Chemistry · Structure of Atom

If the de-broglie wavelength of a particle of mass (m) is 100 times...

If the de-broglie wavelength of a particle of mass (m)(m) is 100 times its velocity. Then, its value in terms of its mass (m)(m) and plank constant (h)(h) is

Options

  1. A110mh\frac{1}{10} \sqrt{\frac{m}{h}}
  2. B10hm10 \sqrt{\frac{h}{m}}
  3. C110hm\frac{1}{10} \sqrt{\frac{h}{m}}
  4. D10mh10 \sqrt{\frac{m}{h}}

Correct answer

B. 10hm10 \sqrt{\frac{h}{m}}

Step-by-step solution

Let the wavelength of given particle =x=x Velocity (v)=x100(v)=\frac{x}{100} Using wavelength formula λ=hmv∴x=hm(x100)x=100hmxx2=100hm⇒x=10hm\begin{aligned} \lambda = \frac{h}{m v} \\ \therefore & x =\frac{h}{m\left(\frac{x}{100}\right)} \\ x & =\frac{100 h}{m x} \\ x^2 & =100 \frac{h}{m} \\ \Rightarrow \quad x & =10 \sqrt{\frac{h}{m}} \end{aligned}
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