JEE Physics Atoms MCQs Set 05

Answer: (d) K-electron capture

Explanation:
1. In K-electron capture the nucleus captures an electron from the K shell
2. The vacancy is filled by an outer electron and a characteristic X-ray is emitted.

Teacher's Note:
1. Characteristic X-rays always follow an inner-shell vacancy.
2. Electron capture is one way of creating such a vacancy.

Answer: (b) the applied potential difference

Explanation:
1. Penetrating power is determined by photon energy, i.e. by the wavelength
2. The wavelength cut-off is fixed by the applied potential difference
3. Filament current changes only the intensity.

Teacher's Note:
1. Hardness depends on voltage.
2. Higher voltage means shorter wavelength and greater penetration.

Answer: (c) X-rays

Explanation:
1. X-rays are electromagnetic waves and travel at c in vacuum
2. Cathode, anode and positive rays are particle beams with speeds much less than c.

Teacher's Note:
1. All electromagnetic radiation moves at the speed of light in vacuum.
2. Particles with mass cannot reach c.

Answer: (d) electron transitions in the target material

Explanation:
1. An incident electron knocks out an inner-shell electron of the target atom
2. An outer electron falls into the vacancy and the energy difference is emitted as the characteristic photon.

Teacher's Note:
1. The photon energy equals the difference of two inner energy levels.
2. The incident electron only creates the vacancy.

Answer: (d) lead

Explanation:
1. Absorption increases with the density and atomic number of the absorber
2. Among the choices, lead (Z = 82) has the highest density and atomic number, so it absorbs most.

Teacher's Note:
1. Lead is used for shielding against X-rays.
2. Light elements like beryllium are almost transparent to X-rays.

Answer: (d) \(\lambda \propto \frac{1}{(Z-1)^2}\)

Explanation:
1. Moseley's law: √ν = a(Z − b), so ν ∝ (Z − 1)² for K_α
2. Since λ = c/ν, λ ∝ 1/(Z − 1)².

Teacher's Note:
1. Frequency grows as the square of (Z − 1).
2. Wavelength is the inverse of frequency.

Answer: (b) 12400/V

Explanation:
1. λmin = hc/eV = 12400 eV Å / (V eV)
2. So λmin = 12400/V Å, with V in volts.

Teacher's Note:
1. 1240/V gives the result in nm.
2. 12.27/√V is the de Broglie wavelength of an electron, not the X-ray cut-off.

Answer: (c) \(\frac{hc}{eV}\)

Explanation:
1. At the cut-off, all the electron's energy goes to one photon: eV = hc/λmin
2. So λmin = hc/(eV).

Teacher's Note:
1. Check the dimensions: hc/E is a length.
2. λmin is inversely proportional to V.

Answer: (c) gamma rays and the ultraviolet region

Explanation:
1. X-ray wavelengths range from about 0.01 Å to 100 Å
2. They lie between the ultraviolet (longer wavelength) and gamma rays (shorter wavelength).

Teacher's Note:
1. Order by decreasing wavelength: radio, microwave, infrared, visible, UV, X-ray, γ.
2. X-rays and γ-rays overlap in wavelength.

Answer: (c) \(\frac{eV}{h}\)

Explanation:
1. eV = hν_max
2. ν_max = eV/h.

Teacher's Note:
1. Maximum frequency corresponds to the minimum wavelength.
2. Frequency in Hz = energy in joules / h.

Answer: (a) the voltage applied to the tube

Explanation:
1. λmin = hc/eV depends only on the applied voltage
2. It does not depend on current or target.

Teacher's Note:
1. The current only changes the intensity.
2. The target material fixes the characteristic lines only.

Answer: (a) increasing the filament current

Explanation:
1. More filament current means more electrons per second reaching the target
2. More electrons produce more photons, so intensity increases.

Teacher's Note:
1. Intensity is the number of photons per second.
2. Target potential changes the quality (hardness).

Answer: (d) 3 × 10⁸ m/s

Explanation:
1. X-rays are electromagnetic waves, so their speed in vacuum is c = 3 × 10⁸ m/s
2. The expressions in the other options give speeds of electrons, not of X-rays.

Teacher's Note:
1. The speed of a photon does not depend on its energy.
2. Do not confuse the electron speed with the X-ray speed.

Answer: (b) 6.6 × 10⁻²⁴ kg m/s

Explanation:
1. p = h/λ = 6.6 × 10⁻³⁴/10⁻¹⁰ = 6.6 × 10⁻²⁴ kg m/s.

Teacher's Note:
1. Photon momentum is h/λ.
2. Check the unit: J s / m = kg m/s.

Answer: (c) x × 5000 eV

Explanation:
1. E ∝ 1/λ
2. The wavelength is 5000 times smaller, so the energy is 5000 times larger: 5000x eV.

Teacher's Note:
1. Energy is inversely proportional to wavelength.
2. 12400/5000 ≈ 2.5 eV, and 12400/1 = 12400 eV is 5000 times that.

Answer: (a) 1.602 × 10⁻¹⁷ joules

Explanation:
1. Kinetic energy = eV = 100 eV = 100 × 1.602 × 10⁻¹⁹ J = 1.602 × 10⁻¹⁷ J.

Teacher's Note:
1. 1 eV = 1.602 × 10⁻¹⁹ J.
2. Other options give a wrong magnitude.

Answer: (d) 0.124 Å

Explanation:
1. The most energetic photon has the cut-off wavelength
2. λ = 12400/10⁵ = 0.124 Å.

Teacher's Note:
1. Most energetic means shortest wavelength.
2. Use E in eV with hc = 12400 eV Å.

Answer: (c) the frequency is higher

Explanation:
1. Hard X-rays have a short wavelength and a high photon energy
2. Since c = νλ, a short wavelength means a high frequency.

Teacher's Note:
1. Soft X-rays have longer wavelengths.
2. Hardness is about the energy of photons, not the number of photons.

Answer: (a) X-rays are produced

Explanation:
1. Rapid deceleration of fast electrons produces bremsstrahlung and characteristic X-rays
2. A target of high melting point withstands the heat generated.

Teacher's Note:
1. A high melting point metal such as tungsten is used.
2. Only about 1% of the energy becomes X-rays; the rest is heat.

Answer: (a) increasing the potential difference between anode and cathode

Explanation:
1. Higher voltage gives photons of higher energy and shorter wavelength
2. These are absorbed less, so they penetrate more.

Teacher's Note:
1. Filament current changes only the intensity.
2. Hardness increases with voltage.

Answer: (a) n = 2 to n = 1

Explanation:
1. K lines are emitted when a vacancy in the K shell (n = 1) is filled
2. K_α is the transition from the L shell (n = 2) to the K shell (n = 1).

Teacher's Note:
1. K_β is n = 3 to n = 1.
2. L_α is n = 3 to n = 2.

Answer: (c) the transition of electrons in heavy target atoms from a high to a low energy level

Explanation:
1. An inner electron is knocked out by the bombarding electron
2. An electron from a higher level falls into the vacancy and emits a photon of definite energy.

Teacher's Note:
1. Characteristic X-rays have fixed energies equal to level differences.
2. Collision energy transfer only creates the vacancy.

Answer: (b) λmin to ∞, where λmin > 0

Explanation:
1. The continuous spectrum has a sharp short-wavelength limit λmin = hc/eV, which is above zero
2. There is no sharp upper limit; the intensity just falls at long wavelengths, so the values extend towards ∞.

Teacher's Note:
1. Zero wavelength would need infinite energy.
2. The cut-off wavelength is fixed by the voltage.