Physics Q43 – JEE-MAIN 2026

Home Physics Dual Nature of MatterQuestion #73

An electron is travelling with a velocity

v

in free space and when it enters a medium, its velocity is reduced by

20 %

. The de Broglie wavelength of electron in the medium is

α λ_{0}

, where

λ_{0}

is its de Broglie wavelength in free space. The value of

α

is _______.

Clue 1 of 3: De Broglie Wavelength Concept

The de Broglie wavelength of a particle is inversely proportional to its momentum.

🧠 Full Solution Path

Step 1: Determine the velocity in the medium✦ Active

The initial velocity of the electron in free space is $v$ . When it enters the medium, its velocity is reduced by $20 %$ . Therefore, the new velocity in the medium, $v^{'}$ , is:

v^{'} = v - 0.20 v = 0.8 v

Step 2: Express de Broglie wavelengths○ Expand

The de Broglie wavelength in free space, $λ_{0}$ , is given by:

λ_{0} = \frac{h}{m v}

The de Broglie wavelength in the medium, $λ_{m}$ , is given by:

λ_{m} = \frac{h}{m v^{'}}

Substitute $v^{'} = 0.8 v$ into the expression for $λ_{m}$ :

λ_{m} = \frac{h}{m (0.8 v)} = \frac{1}{0.8} (\frac{h}{m v})

Since $λ_{0} = \frac{h}{m v}$ , we can write:

λ_{m} = \frac{1}{0.8} λ_{0}

Step 3: Calculate the value of

α

○ Expand

We are given that the de Broglie wavelength in the medium is $α λ_{0}$ . Comparing this with our derived expression:

α λ_{0} = \frac{1}{0.8} λ_{0}

Therefore, the value of $α$ is:

α = \frac{1}{0.8} = \frac{10}{8} = \frac{5}{4} = 1.25

💡 Teacher's Secret Hint

Remember that de Broglie wavelength is inversely proportional to velocity. A decrease in velocity leads to an increase in wavelength.

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Physics Question 43 – JEE-MAIN 2026

Clue 1 of 3: De Broglie Wavelength Concept

🧠 Full Solution Path