Answer
384.6k+ views
Hint: A light is made to fall on a metal and electrons are ejected from it as photons having energy collide with electrons and transfer their energy to them due to which they eject out. We can use Einstein’s equation for photoelectric emission and substitute corresponding values to calculate the cut-off voltage. Convert the units as required.
Formula used:
$K=h\nu -W$
Complete answer:
When light falls on a metal, the photons of the light possesses energy and hence when they collide with the electrons of the metal, they transfer their energy due to which the electrons are ejected out.
The minimum energy required to eject an electron is known as the work function of the metal.
Einstein’s equation for photoelectric effect is given as-
$K=h\nu -W$
Here, $K$ is the kinetic energy
$h$ is Planck’s constant
$\nu $ is the frequency of light
$W$ is the work function
From the above equation,
$\begin{align}
& eV=h\nu -h{{\nu }_{0}} \\
& \Rightarrow V=\dfrac{h(\nu -{{\nu }_{0}})}{e} \\
\end{align}$
Given, $e=1.6\times {{10}^{-19}}$, ${{\nu }_{0}}=3.3\times {{10}^{14}}Hz$, $\nu =8.2\times {{10}^{14}}Hz$, $h=6.6\times {{10}^{-34}}$
In the above equation, we substitute given values to get,
$\begin{align}
& V=\dfrac{6.6\times {{10}^{-34}}(8.2\times {{10}^{14}}-3.2\times {{10}^{14}})}{1.6\times {{10}^{-19}}} \\
& \Rightarrow V=10.56\times {{10}^{-1}}(8.2-3.2) \\
& \Rightarrow V=5.28V \\
& \therefore V\approx 5V \\
\end{align}$
Therefore, the cut-off voltage for photoelectron emission is nearly equal to $5V$.
Hence, the correct option is (C).
Note:
The voltage is applied opposite to the motion of electrons to bring them to rest. That is why; this voltage is known as the cut-off voltage. The energy of the photons is directly proportional to the frequency of light and inversely proportional to the wavelength. It is independent of the intensity of light.
Formula used:
$K=h\nu -W$
Complete answer:
When light falls on a metal, the photons of the light possesses energy and hence when they collide with the electrons of the metal, they transfer their energy due to which the electrons are ejected out.
The minimum energy required to eject an electron is known as the work function of the metal.
Einstein’s equation for photoelectric effect is given as-
$K=h\nu -W$
Here, $K$ is the kinetic energy
$h$ is Planck’s constant
$\nu $ is the frequency of light
$W$ is the work function
From the above equation,
$\begin{align}
& eV=h\nu -h{{\nu }_{0}} \\
& \Rightarrow V=\dfrac{h(\nu -{{\nu }_{0}})}{e} \\
\end{align}$
Given, $e=1.6\times {{10}^{-19}}$, ${{\nu }_{0}}=3.3\times {{10}^{14}}Hz$, $\nu =8.2\times {{10}^{14}}Hz$, $h=6.6\times {{10}^{-34}}$
In the above equation, we substitute given values to get,
$\begin{align}
& V=\dfrac{6.6\times {{10}^{-34}}(8.2\times {{10}^{14}}-3.2\times {{10}^{14}})}{1.6\times {{10}^{-19}}} \\
& \Rightarrow V=10.56\times {{10}^{-1}}(8.2-3.2) \\
& \Rightarrow V=5.28V \\
& \therefore V\approx 5V \\
\end{align}$
Therefore, the cut-off voltage for photoelectron emission is nearly equal to $5V$.
Hence, the correct option is (C).
Note:
The voltage is applied opposite to the motion of electrons to bring them to rest. That is why; this voltage is known as the cut-off voltage. The energy of the photons is directly proportional to the frequency of light and inversely proportional to the wavelength. It is independent of the intensity of light.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)