(B) The de Broglie wavelength is given by $\lambda = \frac{h}{\sqrt{3mk_BT}}$.Here,$m = 9.11 \times 10^{-31} \ kg$,$k_B = 1.38 \times 10^{-23} \ J/K$,

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(B) The de Broglie wavelength is given by $\lambda = \frac{h}{\sqrt{3mk_BT}}$.Here,$m = 9.11 \times 10^{-31} \ kg$,$k_B = 1.38 \times 10^{-23} \ J/K$,and $T = 27 + 273 = 300 \ K$.Substituting these values:$\lambda = \frac{6.63 \times 10^{-34}}{\sqrt{3 \times (9.11 \times 10^{-31}) \times (1.38 \times 10^{-23}) \times 300}}$$\lambda \approx 6.2 \times 10^{-9} \ m$.The mean distance between two electrons is $r = 2 \times 10^{-10} \ m$.The ratio is $\frac{r}{\lambda} = \frac{2 \times 10^{-10}}{6.2 \times 10^{-9}} \approx 0.03$.

Class 12 Physics Dual Nature of Radiation and matter Matter Waves and de Broglie Wavelength

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The de Broglie wavelength of an electron in a metal at $27^{\circ}C$ is compared with the given mean distance between two electrons in the metal,which is $2 \times 10^{-10} \ m$. The ratio of the mean distance to the de Broglie wavelength is approximately:

A
$1.03$
B
$0.03$
C
$0.09$
D
$1.08$

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Dual Nature of Radiation and matter

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Matter Waves and de Broglie Wavelength

An electron accelerated through a potential difference $V_1$ has a de-Broglie wavelength $\lambda$. When the potential is changed to $V_2$,its de-Broglie wavelength increases by $50 \%$. The value of $\left(\frac{V_1}{V_2}\right)$ is

MediumMHT CET 2023

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An $\alpha$-particle moves in a circular path of radius $0.83\, cm$ in the presence of a magnetic field of $0.25\, Wb/m^2$. The de Broglie wavelength associated with the particle will be .............. $\mathring{A}$.

DifficultAIPMT 2012

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The de-Broglie wavelength associated with a hydrogen molecule moving with a thermal velocity of $3 \ km/s$ will be ............ $\mathring{A}$.

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An electron microscope uses electrons of $40 \ keV$. The de Broglie wavelength associated with these electrons is approximately:

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Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths are $\lambda_1$ and $\lambda_2$,their de Broglie wavelength in the frame of reference attached to their centre of mass is

DifficultJEE MAIN 2018

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The de Broglie wavelength of an electron in a metal at $27^{\circ}C$ is compared with the given mean distance between two electrons in the metal,which is $2 \times 10^{-10} \ m$. The ratio of the mean distance to the de Broglie wavelength is approximately:

Similar Questions

An electron accelerated through a potential difference $V_1$ has a de-Broglie wavelength $\lambda$. When the potential is changed to $V_2$,its de-Broglie wavelength increases by $50 \%$. The value of $\left(\frac{V_1}{V_2}\right)$ is

An $\alpha$-particle moves in a circular path of radius $0.83\, cm$ in the presence of a magnetic field of $0.25\, Wb/m^2$. The de Broglie wavelength associated with the particle will be .............. $\mathring{A}$.

The de-Broglie wavelength associated with a hydrogen molecule moving with a thermal velocity of $3 \ km/s$ will be ............ $\mathring{A}$.

An electron microscope uses electrons of $40 \ keV$. The de Broglie wavelength associated with these electrons is approximately:

Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths are $\lambda_1$ and $\lambda_2$,their de Broglie wavelength in the frame of reference attached to their centre of mass is

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