MHT CET · Physics · Dual Nature of Matter
Graph shows the variation of de-Broglie wavelength \(\lambda\) versus \(\frac{1}{\sqrt{V}}\) where \(V\) is the accelerating potential for four particles, P, Q, R, S carrying same charge but of mass \(m_1, m_2, m_3, m_4\). Which one represents a particle of smaller mass?
- A \(m_4\)
- B \(m_1\)
- C \(m_3\)
- D \(m_2\)
Answer & Solution
Correct Answer
(A) \(m_4\)
Step-by-step Solution
Detailed explanation
De-broglie wavelength,
\(\lambda=\frac{h}{p}\)
Kinetic energy :
\(\begin{aligned}
& K=\frac{p^2}{2 m}=q V \\
& \lambda=\frac{h}{\sqrt{2 m q V}}
\end{aligned}\)
Slope of straight line
\(\tan \theta=\frac{h}{\sqrt{2 m q}}\)
Hence, more is slope of line, less is the mass.
\(\lambda=\frac{h}{p}\)
Kinetic energy :
\(\begin{aligned}
& K=\frac{p^2}{2 m}=q V \\
& \lambda=\frac{h}{\sqrt{2 m q V}}
\end{aligned}\)
Slope of straight line
\(\tan \theta=\frac{h}{\sqrt{2 m q}}\)
Hence, more is slope of line, less is the mass.
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