Test: Bragg’s Law - Chemistry MCQ

Concept:
Bragg’s Law states that when an X-ray beam are allowed to scatter through a crystalline surface, its angle of incidence θ will reflect with some angle of scattering θ. And when the path difference d is equal to a whole number n, of wavelength.
It can be represented as
2dsinθ  =nλ
Calculation:
Given:
d = 0.18 nm, n = 1, θ = 22°
⇒ 2 × 0.18 × sin 22° = 1 ⋅ λ
⇒ λ = 0.07488 nm

CONCEPT:
The wavelength of any charged particle due to its motion is called the de-Broglie wavelength.
When a charged particle is accelerated in a potential difference the energy gained by the particle is given by:
Energy (E) = e × V
Where V is the potential difference and q is a charge.
The de-Broglie wavelength of charge particle (λ_d) is given by:

Where E is energy, h is Planck constant, m is the mass of the charged particle
EXPLANATION:
De-Broglie wavelength when a charge q is accelerated by a potential difference of V volts is

For cut off wavelength of X-rays, we have


From Eqs, i) and ii), we get

For electron q/m = 1.8 x 10¹¹C/kg (given).
Substituting the values the desired ratio is

Concept:
Bragg’s Law states that when an X-ray beam are allowed to scatter through a crystalline surface, its angle of incidence θ will reflect with some angle of scattering θ. And when the path difference d is equal to a whole number n, of wavelength.
It can be represented as
2dsinθ  =nλ
Calculation:
Given:
d = 0.18 nm, n = 1, θ = 22°
From Bragg’s law:
2d sin θ = nλ
2 × 0.18 × sin 22° = 1 ⋅ λ
λ = 0.13464 nm

X-rays aren't deflected by electrons and magnetic  fields because x-rays do not carry and charge. They  are electro-magnetic radiations and therefore  cannot be deflected by electronic or any magnetic  fields. 
EXTRA POINTS:
1. X-rays: An electromagnetic wave with wavelengths from 0.1 Å to 100 Å called X-rays.
2. X-rays were discovered by WC Roentgen in 1895 and he was later awarded with Nobel Prize in 1901. So option 4 is correct.
3. He named that new unknown type of radiation as X-rays.
4. X-rays are the second most energetic radiations in the Electromagnetic Spectrum following Gamma rays.
5. The wavelength of these rays ranges from 10-11 to 10-8 m and the frequency is around 3 x 1016 - 3 x 1019.
6. Therefore these are very shortwave and high energy EM radiations (travelling with the speed of light).
7. X-rays are widely used in medical diagnosis and Astronomy.

Concept:
Bragg’s Law states that when an X-ray beam are allowed to scatter through a crystalline surface, its angle of incidence θ will reflect with some angle of scattering θ. And when the path difference d is equal to a whole number n, of wavelength.
It can be represented as
2dsinθ  =nλ
Calculation:
Given:
λ = 1.315 Å, n = 1,
2θ = 60°
θ = 30°
From Bragg’s law:
2d sin θ = nλ
2 × d × sin 30° = 1 × 1.315

Concept:
Bragg’s Law:
Bragg's Law relates the angle θ (at which there is a maximum in diffracted intensity ) to the wavelength of X-rays and the interlayer distance d between the planes of atoms/ions/molecules in the lattice. Condition for constructive interference (maxima in the reflected).
nλ = 2d sinθ
λ = Wavelength of the X-ray
d = distance of crystal layers
θ = incident angle (the angle between the incident plane and the scattering plane)
n = integer (order)
Calculation:
Given:
d = 4.5 × 10^-10 m, θ = 30°, n = 2
We know that,
nλ = 2d sin θ
∴ 2λ = 2 × 4.5 × 10^-10 × sin 30°
λ = 2.25 × 10^-10 m

CONCEPT:

• X-ray crystallography: It is the technique of determining the molecular and atomic structure of a crystal.
• X-ray beams are used to determine the structure of the crystal.
• The crystal diffracts the X-ray beams and the intensities and angle of diffraction of these diffracted beams is studied to estimate the structure of the crystal.

EXPLANATION:

• The diffraction of light is used in X-ray crystallography.
• X-rays diffracted from the crystal are studied to determine the structure of the crystal.
• X-ray crystallography is not used to find the physical properties of liquids.

CONCEPT:

• X-ray crystallography: It is the technique of determining the molecular and atomic structure of a crystal.
• X-ray beams are used to determine the structure of the crystal.
• The crystal diffracts the X-ray beams and the intensities and angle of diffraction of these diffracted beams are studied to estimate the structure of the crystal.

EXPLANATION:

• The diffraction of light is used in X-ray crystallography.
• X-rays diffracted from the crystal are studied to determine the structure of the crystal.

Concept:
In X-ray scattering
nλ = 2d sin θ

where d = distance between atomic planes, θ = glancing angle, λ = wavelength
Calculation:
Given:
For line A:
n₁ = 2, θ₁ = 60^o, λ₁ = ?
For line B;
n₂ = 3, θ₂ = 30^o, λ₂ = 0.25 nm
Distance between atomic planes d1 and d2 is equal for same crystal i.e.;
d₁ = d₂ = d
From equation (1);


On solving we'll get;
λ₁ = 0.649 nm ≈ 0.65 nm

X-rays:

• X-rays are electromagnetic radiations.
• They are high-energy radiations that are not produced by the movement of charges.
• This radiation has a high penetrating nature and is therefore used in scanning.
• Similar to heat radiations, these rays are also radiations.
• The small number of X-rays are accompanied by the sunlight that reaches the Earth.
• Electric fields are produced by charged particles and these fields interact with charged particles.
• Electrically charged particle motion produces a magnetic field.