An electron and photon have same energy 100eV. Which has greater … - Vidyadip

Question

An electron and photon have same energy 100eV. Which has greater associated wavelength?

✓

Answer

De-Broglie wavelength associated with electron,

$\lambda_\text{e}=\frac{\text{h}}{\sqrt{2\text{mE}_\text{e}}}\Rightarrow\ \text{E}_\text{}e=\frac{\text{h}^2}{2\text{m}\lambda^2_\text{e}}\dots(\text{i})$

Also wavelength of photon of energy E_ph is,

$\text{E}_\text{ph}=\frac{\text{hc}}{\lambda_{\text{ph}}}\Rightarrow\ \text{E}^2_{\text{ph}}=\frac{\text{h}^2\text{c}^2}{\lambda^2_\text{ph}}\dots(\text{ii})$

Given E_e = E_ph = E (say) = 100eV

Dividing (ii) by (i) and using (iii), we get

$\text{E}=\frac{\frac{\text{h}^2\text{c}^2}{\lambda^2_\text{ph}}}{\frac{\text{h}^2}{2\text{m}\lambda^2_\text{e}}}$ or $\text{E}=\frac{2\text{mc}^2\lambda^2_\text{e}}{\lambda^2_{\text{ph}}}$

$\therefore\ \frac{\lambda_\text{e}}{\lambda_{\text{ph}}}=\sqrt{\frac{\text{E}}{2\text{mc}^2}}$

As $\text{E}=100\text{eV } 2\text{mc}^2\cong1\text{MeV}$

$\therefore\ \text{E}<<2\text{mc}^2\Rightarrow\ \lambda_\text{e}<\lambda_\text{ph}$

That is, wavelength associated with photon is greater as compared to electron of same energy.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Dual Nature of Radiation and Matter→Dual Nature of Radiation and Matter — all question types→Physics STD 12 Science question papers→Bihar Board STD 12 Science question papers→Bihar Board question paper generator→

Similar questions

Draw a schematic arrangement for winding of primary and secondary coils in a transformer with the two coils on separate limbs of the core. State its underlying principle and find the relation between the primary and secondary voltages in terms of the number of turns of the primary and secondary windings. How are the currents in the primary and secondary coils related to the voltages in the case of an ideal transformer?

Explain briefly with the help of necessary diagrams, the forward and the reverse biasing of a p-n junction diode. Also draw their characteristic curves in the two cases.

Assume that the mass of a nucleus is approximately given by M = Am_p where A is the mass number. Estimate the density of matter in kg/m³ inside a nucleus. What is the specific gravity of nuclear matter?

In a p-n junction, a potential barrier of 250meV exists across the junction. A hole with a kinetic energy of 300meV approaches the junction. Find the kinetic energy of the hole when it crosses the junction if the hole approached the junction.

From the p-side.
From the n-side.

a. Differentiate between nuclear fission and nuclear fusion.
b. Deuterium undergoes fusion as per the reaction:
${ }_1^2 H +{ }_1^2 H \longrightarrow{ }_2^3 He +{ }_0^1 n +3.27 MeV$
Find the duration for which an electric bulb of 500 W can be kept glowing by the fusion of 100 g of deuterium.

Define an equipotential surface. Draw equipotential surface:

In the case of a single point charge and,
In a constant electric field in Z-direction.

Why the equipotential surfaces about a single charge are not equidistant?

Can electric field exist tangential to an equipotential surface? Give reason.

The rest distance between Patna and Delhi is 1000km. A nonstop train travels at 360km/h:

What is the distance between Patna and Delhi in the train frame?
How much time elapses in the train frame between Patna and Delhi?

The maximum speed and acceleration of a particle executing simple harmonic motion are 10cm/s and 50cm/s². Find the position(s) of the particle when the speed is 8cm/s.

What will be the effect on placing a metal foil between the plates of a parallel plate capacitor on its capacitance?

Suppose we have 12 protons and 12 neutrons. We can assemble them to form either a :uMg nucleus or two 12C nuclei. In which of the two cases more energy will be liberated?