Question:
Light of frequency \(7.21×10^{14}Hz\) is incident on a metal surface. Electrons with a maximum speed of \(6.0×10^5 m/s\) are ejected from the surface.What is the threshold frequency for photoemission of electrons?
Light of frequency \(7.21×10^{14}Hz\) is incident on a metal surface. Electrons with a maximum speed of \(6.0×10^5 m/s\) are ejected from the surface.What is the threshold frequency for photoemission of electrons?
Updated On: Sep 29, 2023
Hide Solution
Verified By Collegedunia
Solution and Explanation
The correct answer is: \(4.738×10^{14}Hz\)
Frequency of the incident photon, \(v=488nm=488×10^{-9}m\)
Maximum speed of the electrons, \(v=6.0×10^5m/s\)
Planck’s constant, \(h=6.626×10^{−34}Js\)
Mass of an electron, \(m=9.1×10^{−31}kg\)
For threshold frequency \(ν_0\), the relation for kinetic energy is written as:
\(\frac{1}{2}mv^2=h(v-v_0)\)
\(v_0=v-\frac{mv^2}{2h}\)
\(=7.21×10^{14}-\frac{(9.1×10^{-31})×(6×10^5)^2}{2×(6.626×10^{-34})}\)
\(=7.21×10^{14}-2.472×10^{14}\)
\(=4.738×10^{14}Hz\)
Therefore,the threshold frequency for the photoemission of electrons is \(4.738×10^{14}Hz\)
Frequency of the incident photon, \(v=488nm=488×10^{-9}m\)
Maximum speed of the electrons, \(v=6.0×10^5m/s\)
Planck’s constant, \(h=6.626×10^{−34}Js\)
Mass of an electron, \(m=9.1×10^{−31}kg\)
For threshold frequency \(ν_0\), the relation for kinetic energy is written as:
\(\frac{1}{2}mv^2=h(v-v_0)\)
\(v_0=v-\frac{mv^2}{2h}\)
\(=7.21×10^{14}-\frac{(9.1×10^{-31})×(6×10^5)^2}{2×(6.626×10^{-34})}\)
\(=7.21×10^{14}-2.472×10^{14}\)
\(=4.738×10^{14}Hz\)
Therefore,the threshold frequency for the photoemission of electrons is \(4.738×10^{14}Hz\)
Was this answer helpful?
0
0
Top Questions on Dual nature of radiation and matter
- Atomic spectral emission lines of hydrogen atom are incident on a zinc surface. The lines which can emit photoelectrons from the surface are members of:
- CBSE CLASS XII - 2025
- Physics
- Dual nature of radiation and matter
- Radiations of two frequencies are incident on a metal surface of work function 2.0 eV one by one. The energies of their photons are 2.5 eV and 4.5 eV respectively. Find the ratio of the maximum speed of the electrons emitted in the two cases.
- CBSE CLASS XII - 2025
- Physics
- Dual nature of radiation and matter
- Whether the total mass of nuclei increases, decreases or remains unchanged?
- CBSE CLASS XII - 2025
- Physics
- Dual nature of radiation and matter
- Does the process require energy or produce energy?
- CBSE CLASS XII - 2025
- Physics
- Dual nature of radiation and matter
- When a photon of suitable frequency is incident on a metal surface, a photoelectron is emitted from it. If the frequency is below a threshold frequency (ν0) for the surface, no photoelectron is emitted. For a photon of frequency ν (ν > ν0), the kinetic energy of the emitted photoelectron is:
Km = h(ν − ν0)
The photocurrent can be stopped by applying a potential V0, called the "stopping potential," on the anode. Thus, the maximum kinetic energy of photoelectrons is:
Km = eV0 = h(ν − ν0)
The experimental graph between V0 and ν for a metal is shown in the figure. This is a straight line of slope m.
- CBSE CLASS XII - 2025
- Physics
- Dual nature of radiation and matter
View More Questions
Questions Asked in CBSE CLASS XII exam
- Using integration, find the area of the region bounded by the line \[ y = 5x + 2, \] the \( x \)-axis, and the ordinates \( x = -2 \) and \( x = 2 \).
- CBSE CLASS XII - 2025
- Evaluation of Definite Integrals by Substitution
- In case the total cost of a machine less installation charges is greater than Rs 2,00,000, then 20% depreciation is charged, and if total cost of the machine is less than Rs 2,00,000 then 10% depreciation is charged.
Write the steps to create the 'IF' function using the Formula tab and dialogue box on a given spreadsheet. Also, write the syntax of the result.- CBSE CLASS XII - 2025
- Computerised Accounting
- State the advantages of 'Pivot Table' report.
- CBSE CLASS XII - 2025
- Basic Knowledge of Excel
- To see all available shape styles which of the following button is clicked ?
- CBSE CLASS XII - 2025
- Computerised Accounting
- Null value is the special value which represents :
- CBSE CLASS XII - 2025
- Computerised Accounting
View More Questions
Concepts Used:
Photoelectric Effect
When light shines on a metal, electrons can be ejected from the surface of the metal in a phenomenon known as the photoelectric effect. This process is also often referred to as photoemission, and the electrons that are ejected from the metal are called photoelectrons.
Photoelectric Effect Formula:
According to Einstein’s explanation of the photoelectric effect :
The energy of photon = energy needed to remove an electron + kinetic energy of the emitted electron
i.e. hν = W + E
Where,
- h is Planck’s constant.
- ν is the frequency of the incident photon.
- W is a work function.
- E is the maximum kinetic energy of ejected electrons: 1/2 mv².
Laws of Photoelectric Effect:
- The photoelectric current is in direct proportion to the intensity of light, for a light of any given frequency; (γ > γ Th).
- There exists a certain minimum (energy) frequency for a given material, called threshold frequency, below which the discharge of photoelectrons stops completely, irrespective of how high the intensity of incident light is.
- The maximum kinetic energy of the photoelectrons increases with the increase in the frequency (provided frequency γ > γ Th exceeds the threshold limit) of the incident light. The maximum kinetic energy is free from the intensity of light.
- The process of photo-emission is an instantaneous process.