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GUJCET · Physics · Dual Nature of Radiation and Matter
What is the de-Broglie wavelength associated with an electron moving with a speed of \(6.4 \times\) \(10^{6} \mathrm{~m} / \mathrm{s}^{-1}\) ?
\(\left(m_{e}=9.11 \times 10^{-31} \mathrm{~kg}, h=6.63 \times 10^{-34} \mathrm{Js}\right)\)
- A 0.124 nm
- B 0.114 nm
- C 0.135 nm
- D 0.145 nm
Answer & Solution
Correct Answer
(B) 0.114 nm
Step-by-step Solution
Detailed explanation
(B) 0.114 nm
de-Broglie wavelength,
\(
\begin{aligned}
& \lambda=\frac{h}{m v} \\
& \lambda=\frac{6.63 \times 10^{-34}}{9.11 \times 10^{-31} \times 6.4 \times 10^{6}} \\
& \lambda=0.1137 \times 10^{-9} \mathrm{~m} \\
& \lambda \approx 0.114 \mathrm{~nm}
\end{aligned}
\)
de-Broglie wavelength,
\(
\begin{aligned}
& \lambda=\frac{h}{m v} \\
& \lambda=\frac{6.63 \times 10^{-34}}{9.11 \times 10^{-31} \times 6.4 \times 10^{6}} \\
& \lambda=0.1137 \times 10^{-9} \mathrm{~m} \\
& \lambda \approx 0.114 \mathrm{~nm}
\end{aligned}
\)
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