Conductivity of a photodiode starts changing only if the wavelength of incident light is less than 660 nm . The band gap of photodiode is found to be $\left(\frac{\mathrm{X}}{8}\right) \mathrm{eV}$. The value of X is : (Given, $\mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$ )

JEE Main · 2024 · 01 Feb 2024 · Shift 2 · Modern Physics

Conductivity of a photodiode starts changing only if the wavelength of incident light is less than 660 nm . The band gap of photodiode is found to be

(\frac{X}{8}) eV

. The value of X is :
(Given,

h = 6.6 \times 1 0^{- 34} Js, e = 1.6 \times 1 0^{- 19} C

)

(A)15✓ Correct
(B)11
(C)13
(D)21

Answer: (A)

Solution

The threshold wavelength marks the photon energy equal to the band gap:

E_{g} = \frac{h c}{λ}

. With

λ = 660

nm,

E_{g} = \frac{6.6 \times 1 0 ^{- 34} \times 3 \times 1 0 ^{8}}{660 \times 1 0 ^{- 9}}

J. Converting to electron-volts by dividing by

e = 1.6 \times 1 0^{- 19}

E_{g} = \frac{6.6 \times 1 0 ^{- 34} \times 3 \times 1 0 ^{8}}{660 \times 1 0 ^{- 9} \times 1.6 \times 1 0 ^{- 19}} = \frac{15}{8} eV

. Comparing with the given form

\frac{X}{8}

eV gives

X = 15

JEE Main · 2024 · 01 Feb 2024 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Modern Physics →

More JEE Main questions on Modern Physics

7.9 MeV α-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) ______ m.
[ $\frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9}$ Nm²/C² and electron charge $= 1.6 \times 1 0^{- 19}$ C]
JEE Main 2026View solution →
The minimum frequency of photon required to break a particle of mass 15.348 amu into $4 α$ particles is ______ kHz.
[mass of He nucleus = 4.002 amu, $1$ amu $= 1.66 \times 1 0^{- 27}$ kg, $h = 6.6 \times 1 0^{- 34}$ J.s and $c = 3 \times 1 0^{8}$ m/s]
JEE Main 2026View solution →
The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly $____$ nm.
JEE Main 2026View solution →
Light is incident on a metallic plate having work function $110 \times 1 0^{- 20} J$ . If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ______ $rad / s$ . ( …
JEE Main 2026View solution →
The energy of an electron in an orbit of the Bohr's atom is $- 0.04 E_{0} eV$ where $E_{0}$ is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck's constant, then …
JEE Main 2026View solution →
A particle having electric charge $3 \times 1 0^{- 19} C$ and mass $6 \times 1 0^{- 27} kg$ is accelerated by applying an electric potential of 1.21 V . Wavelength of the matter wave associated with the particle is $α \times 1 0^{- 12} m$ . The va …
JEE Main 2026View solution →