Integer Answer Type Questions for JEE: Dual Nature of Matter & Radiation | Chapter-wise Tests for JEE Main & Advanced PDF Download

Q.1. Light of wavelength 4000 Å falls on a photosensitive metal and a negative 2V potential stops the emitted electrons. The work function of the material (in eV) is approximately.
(h = 6.6  x 10^-34 Js, e = 1.6 x 10^-19 C, c = 3 x 10⁸ ms^-1 )

Ans. 1.1 eV
Energy of incident light   = 3.09 eV
Stopping potential is –2V so K_max = 2 eV
Hence by using E = W₀ + K_max ; W₀ = 1.09 eV » 1.1 eV

Q.2. The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission form this substance is approximately 

Ans. 310 nm

= 3100 Å
= 310 nm

Q.3. 4 eV is the energy of the incident photon and the work function is 2eV. What is the stopping potential?

Ans. 2 volts
E = W₀ + eV₀
⇒ 4eV = 2eV + eV0
⇒ V₀ = 2 volt

Q.4. Light from a hydrogen discharge tube is incident on the cathode of a photoelectric cell the work function of the cathode surface is 4.2 eV. In order to reduce the photocurrent to zero the voltage of the anode relative to the cathode must be made

Ans. -9.4 V
E = W₀ + eV₀
For hydrogen atom, E = +13.6 eV
∴ + 13.6 = 4.2 + eV₀
⇒
Potential at anode = –9.4 V

Q.5. The largest distance between the interatomic planes of a crystal is 10^–7 cm. The upper limit for the wavelength of Xrays which can be usefully studied with this crystal is

Ans. 20 Å
Bragg's law, 2dsinθ = nλ or
For maximum wavelength, n_min = 1, (sinθ)_max = 1
∴

Q.6. The wavelength of K_α X-rays produced by an X-ray tube is 0.76 Å. The atomic number of the anode material of the tube is 

Ans. 41
For K_α  X−ray line,

⇒
With reference to given data,
λ_α = 0.76A˚ = 0.76 × 10⁻¹⁰ m
R = 1.097 × 10⁷ m
Putting these values in equation (1)

⇒Z − 1 = 40 ⇒ Z=  41
Hence (B) is correct.

Q.7. The K_α X-ray emission line of tungsten occurs at l = 0.021 nm. The energy difference between K and L levels in this atom is about 

Ans. 59 keV

= 59 keV

Q.8. A silver ball of radius 4.8 cm is suspended by a thread in the vacuum chamber. UV light of wavelength 200 nm is incident on the ball for some times during which a total energy of 1 x 10^–7 J falls on the surface. Assuming on an average one out of 10³ photons incident is able to eject electron. The potential on sphere will be 

Ans. 3 V

Number of electrons ejected = 10¹¹ / 10³ = 10⁸
∴
= 3 V

Q.9.  The potential difference across Coolidge tube is 20 kv and 10 mA current flows through the voltage supply. Only 0.5% of the energy carried by electrons striking the target is converted into X-ray. Then the power carried by X-ray beam in watts is –

Ans. 1
P = VI
Total power drawn by tube = P_T = VI = 200 W As 0.5% of energy is carried by electrons power earned by X-ray = 0.5% of P_T = 1W.

Q.10. A hydrogen atom collides inelastically with another stationary hydrogen atom. Before collision both are at ground state and after collision one of them gets excited. The minimum kinetic energy of initial moving hydrogen atom is what times of minimum excitation energy of ground state hydrogen atom.

Ans. 2
According to conservation of momentum

According to conservation of energy

So Ans. is 2