JEE Advanced Physics PYQ: Wave Optics | Previous Year Questions with Solutions

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Q 1 :

A proton has kinetic energy $E = 100 keV$ which is equal to that of a photon. The wavelength of the photon is $λ_{2}$ and that of the proton is $λ_{1}$ . The ratio $\frac{λ_{2}}{λ_{1}}$ is proportional to [2004]

$E^{2}$
$E^{1 / 2}$
$E^{- 1}$
$E^{- 1 / 2}$

(4)

For photon, $λ_{2} = \frac{h c}{E}$ $\dots (i)$

For proton, $λ_{1} = \frac{h}{p} = \frac{h}{\sqrt{2 m E}}$ $∵$ $p = \sqrt{2 m E}$ $\dots (i i)$

$∴$ $\frac{λ_{2}}{λ_{1}} = \frac{h c}{E \times \frac{h}{\sqrt{2 m E}}} \propto E^{- 1 / 2}$

Q 2 :

An $α$ -particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de Broglie wavelengths are $λ_{α}$ and $λ_{p}$ , respectively. The ratio $\frac{λ_{p}}{λ_{α}},$ to the nearest integer, is [2010]

(3)

We know that, $λ = \frac{h}{\sqrt{2 m q V}}$ or, $λ \propto \frac{1}{\sqrt{q m}}$

$∴$ $\frac{λ_{p}}{λ_{α}} = \sqrt{\frac{m_{α} q_{α}}{m_{p} q_{p}}} = \sqrt{\frac{4}{1} \times \frac{2}{1}} = \sqrt{8} \approx 3$

Topic Question Set

Q 1 :

A proton has kinetic energy $E = 100 keV$ which is equal to that of a photon. The wavelength of the photon is $λ_{2}$ and that of the proton is $λ_{1}$ . The ratio $\frac{λ_{2}}{λ_{1}}$ is proportional to [2004]

Q 2 :

An $α$ -particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de Broglie wavelengths are $λ_{α}$ and $λ_{p}$ , respectively. The ratio $\frac{λ_{p}}{λ_{α}},$ to the nearest integer, is [2010]

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Topic Question Set

Q 1 : A proton has kinetic energy E=100 keV which is equal to that of a photon. The wavelength of the photon is λ2 and that of the proton is λ1. The ratio λ2λ1 is proportional to [2004]

Q 2 : An α-particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de Broglie wavelengths are λα and λp, respectively. The ratio λpλα, to the nearest integer, is [2010]

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Q 1 :

A proton has kinetic energy $E = 100 keV$ which is equal to that of a photon. The wavelength of the photon is $λ_{2}$ and that of the proton is $λ_{1}$ . The ratio $\frac{λ_{2}}{λ_{1}}$ is proportional to [2004]

Q 2 :

An $α$ -particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de Broglie wavelengths are $λ_{α}$ and $λ_{p}$ , respectively. The ratio $\frac{λ_{p}}{λ_{α}},$ to the nearest integer, is [2010]