Question:
An electron travelling with velocity \(v\) in free space enters a medium where its velocity is reduced by \(20\%\). The de-Broglie wavelength of the electron in the medium is \(\alpha \lambda_0\), where \(\lambda_0\) is the wavelength in free space. Find the value of \(\alpha\).
An electron travelling with velocity \(v\) in free space enters a medium where its velocity is reduced by \(20\%\). The de-Broglie wavelength of the electron in the medium is \(\alpha \lambda_0\), where \(\lambda_0\) is the wavelength in free space. Find the value of \(\alpha\).
Show Hint
For de-Broglie wavelength:
\[
\lambda = \frac{h}{mv}
\]
If velocity decreases, wavelength increases proportionally.
Updated On: Apr 7, 2026
- \(1.25\)
- \(1.5\)
- \(0.8\)
- \(0.125\)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Concept:
The de-Broglie wavelength is given by
\[
\lambda = \frac{h}{mv}
\]
Thus,
\[
\lambda \propto \frac{1}{v}
\]
So wavelength is inversely proportional to velocity.
Step 1: Determine new velocity in the medium. Velocity decreases by \(20\%\): \[ v_2 = v_0 - 0.2v_0 \] \[ v_2 = 0.8v_0 \]
Step 2: Use inverse proportionality of wavelength and velocity. \[ \lambda \propto \frac{1}{v} \] \[ \frac{\lambda_1}{\lambda_2}=\frac{v_2}{v_1} \] \[ \frac{\lambda_0}{\lambda}=\frac{0.8v_0}{v_0} \] \[ \frac{\lambda_0}{\lambda}=0.8 \]
Step 3: Find wavelength in the medium. \[ \lambda=\frac{\lambda_0}{0.8} \] \[ \lambda=1.25\lambda_0 \] Thus, \[ \alpha=1.25 \] \[ \boxed{\alpha=1.25} \]
Step 1: Determine new velocity in the medium. Velocity decreases by \(20\%\): \[ v_2 = v_0 - 0.2v_0 \] \[ v_2 = 0.8v_0 \]
Step 2: Use inverse proportionality of wavelength and velocity. \[ \lambda \propto \frac{1}{v} \] \[ \frac{\lambda_1}{\lambda_2}=\frac{v_2}{v_1} \] \[ \frac{\lambda_0}{\lambda}=\frac{0.8v_0}{v_0} \] \[ \frac{\lambda_0}{\lambda}=0.8 \]
Step 3: Find wavelength in the medium. \[ \lambda=\frac{\lambda_0}{0.8} \] \[ \lambda=1.25\lambda_0 \] Thus, \[ \alpha=1.25 \] \[ \boxed{\alpha=1.25} \]
Was this answer helpful?
0
0
Top JEE Main Physics Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
View More Questions
Top JEE Main Modern Physics Questions
- A long straight wire of circular cross-section (radius \( a \)) is carrying a steady current \( I \). The current \( I \) is uniformly distributed across this cross-section. The magnetic field is:
- Two sources of light emit with a power of 200 W.The ratio of number of photons of visible light emitted by each source having wavelengths 300 nm and 500 nm respectively, will be :
- A hydrogen atom is bombarded with electrons accelerated through a potential difference of \( V \), which causes excitation of hydrogen atoms. If the experiment is being performed at \( T = 0 \, \text{K} \), the minimum potential difference needed to observe any Balmer series lines in the emission spectra will be\[\frac{\alpha}{10} V,\]where \( \alpha = \, \underline{\hspace{2cm}} \).
- The energy equivalent of 1g of substance is:
- From the statements given below :
(A) The angular momentum of an electron in nth orbit is an integral multiple of h.
(B) Nuclear forces do not obey inverse square law.
(C) Nuclear forces are spin dependent.
(D) Nuclear forces are central and charge independent.
(E) Stability of nucleus is inversely proportional to the value of packing fraction.
Choose the correct answer from the options given below :
View More Questions
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
View More Questions