SATHEE: Atomic Structure 1 Question 27

Atomic Structure 1 Question 27

3. What is the work function of the metal, if the light of wavelength $4000 \AA$ generates photoelectron of velocity $6 \times 10^{5} {ms}^{- 1}$ from it?

(Mass of electron $= 9 \times 10^{- 31} kg$

Velocity of light $= 3 \times 10^{8} {ms}^{- 1}$

Planck’s constant $= 6.626 \times 10^{- 34} Js$

Charge of electron $= 1.6 \times 10^{- 19} {JeV}^{- 1}$ )

(2019 Main, 12 Jan I)

(a) $4.0 eV$

(b) $2.1 eV$

(d) $3.1 eV$

Show Answer

Answer:

Correct Answer: 3. (d)

Solution:

Work function of metal $(ϕ) = h v_{0}$ where, $v_{0} =$ threshold frequency

Also, $\frac{1}{2} m_{e} v^{2} = h v - h v_{0}$

$\begin{aligned} \frac{1}{2} m_{e} v^{2} = h v - ϕ & \frac{1}{2} m_{e} v^{2} = \frac{h c}{λ} - ϕ \end{aligned}$

Given : $λ = 4000 \AA = 4000 \times 10^{- 10} m$

$\begin{aligned} v & = 6 \times 10^{5} {ms}^{- 1}, m_{e} & = 9 \times 10^{- 31} kg, c = 3 \times 10^{8} {ms}^{- 1} h & = 6.626 \times 10^{- 34} Js \end{aligned}$

Thus, on substituting all the given values in Eq. (i), we get

$\begin{aligned} \frac{1}{2} \times 9 \times 10^{- 31} kg \times {(6 \times 10^{5} {ms}^{- 1})}^{2} & = \frac{6.626 \times 10^{- 34} J s \times 3 \times 10^{8} {ms}^{- 1}}{4000 \times 10^{- 10} m} - ϕ & ∴ ϕ = 1.62 \times 10^{- 21} {kgm}^{2} s^{- 2} - 4.96 \times 10^{- 19} J & = 3.36 \times 10^{- 19} J [1 kg m^{2} s^{- 2} = 1 J] & = 2.1 eV \end{aligned}$

Atomic Structure 1 Question 27

3. What is the work function of the metal, if the light of wavelength $4000 \AA$ generates photoelectron of velocity $6 \times 10^{5} {ms}^{- 1}$ from it?

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

Atomic Structure 1 Question 27

3. What is the work function of the metal, if the light of wavelength 4000\AA generates photoelectron of velocity 6×105 ms−1 from it?

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

Menu

3. What is the work function of the metal, if the light of wavelength $4000 \AA$ generates photoelectron of velocity $6 \times 10^{5} {ms}^{- 1}$ from it?