
Find the frequency of a photon of energy 75eV.
Answer
155.4k+ views
Hint: Photon is the smallest quanta of energy. According to the particle nature of light, light behaves as particles and this is confirmed by photoelectric effect, but according to wave nature of light, light behaves as waves and this is confirmed by phenomenon like reflection, refraction etc. We can make use of the Planck quantum formula to solve this problem.
Complete Step by step solution:
Given the energy of photon is $75eV$
We know energy is given by the formula\[E=h\nu \], where h is the Planck’s constant whose value is \[6.6\times {{10}^{-34}}Js\] and v is the frequency.
When the energy is given in electron-Volts, we have to first convert it into Joules.
$E=75eV \\
\Rightarrow E=75\times 1.6\times {{10}^{-19}}J \\
\therefore E=12\times {{10}^{-18}}J \\$
Now we make use of the above-mentioned formula,
$E=12\times {{10}^{-18}}J \\
\Rightarrow hv=12\times {{10}^{-18}} \\
\Rightarrow 6.6\times {{10}^{-34}}\times v=12\times {{10}^{-18}} \\
\Rightarrow v=\dfrac{12\times {{10}^{-18}}}{6.6\times {{10}^{-34}}} \\
\therefore v=1.82\times {{10}^{16}}Hz \\$
So, the frequency comes out to be \[1.82\times {{10}^{16}}Hz\]
Additional Information: From photoelectric effect, Einstein equation is given by \[h\nu =h{{\nu }_{0}}+KE\]
Here \[h\nu \]in the energy of the incident radiation and \[h{{\nu }_{0}}\]is the work function of the metal given.
Note: Here the energy was given in eV, so we first converted it into Joules and then used the formula. But suppose if we had to find the wavelength and the frequency both then we could have use the formula; \[E=\frac{hc}{\lambda }\], where we would have taken E in eV and the value of hc we would have taken 1240 eV-nm. After finding the wavelength in nm we would have converted it into metres, and then we would have used the formula for finding out the frequency.
Complete Step by step solution:
Given the energy of photon is $75eV$
We know energy is given by the formula\[E=h\nu \], where h is the Planck’s constant whose value is \[6.6\times {{10}^{-34}}Js\] and v is the frequency.
When the energy is given in electron-Volts, we have to first convert it into Joules.
$E=75eV \\
\Rightarrow E=75\times 1.6\times {{10}^{-19}}J \\
\therefore E=12\times {{10}^{-18}}J \\$
Now we make use of the above-mentioned formula,
$E=12\times {{10}^{-18}}J \\
\Rightarrow hv=12\times {{10}^{-18}} \\
\Rightarrow 6.6\times {{10}^{-34}}\times v=12\times {{10}^{-18}} \\
\Rightarrow v=\dfrac{12\times {{10}^{-18}}}{6.6\times {{10}^{-34}}} \\
\therefore v=1.82\times {{10}^{16}}Hz \\$
So, the frequency comes out to be \[1.82\times {{10}^{16}}Hz\]
Additional Information: From photoelectric effect, Einstein equation is given by \[h\nu =h{{\nu }_{0}}+KE\]
Here \[h\nu \]in the energy of the incident radiation and \[h{{\nu }_{0}}\]is the work function of the metal given.
Note: Here the energy was given in eV, so we first converted it into Joules and then used the formula. But suppose if we had to find the wavelength and the frequency both then we could have use the formula; \[E=\frac{hc}{\lambda }\], where we would have taken E in eV and the value of hc we would have taken 1240 eV-nm. After finding the wavelength in nm we would have converted it into metres, and then we would have used the formula for finding out the frequency.
Recently Updated Pages
Wheatstone Bridge - Working Principle, Formula, Derivation, Application

Young's Double Slit Experiment Step by Step Derivation

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Chemical Properties of Hydrogen - Important Concepts for JEE Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Degree of Dissociation and Its Formula With Solved Example for JEE

Displacement-Time Graph and Velocity-Time Graph for JEE

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

JEE Advanced 2025 Notes

Electrical Field of Charged Spherical Shell - JEE

Geostationary Satellites and Geosynchronous Satellites - JEE Important Topic
