NDA Physics · Modern Physics

Quantum and Modern EM: X-rays, Semiconductors, Scattering

A grab-bag of modern applications: X-rays (high-energy EM made by stopping fast electrons), semiconductors (p-type and n-type materials that follow Ohm's law), and the Raman effect (light changing frequency when scattered).

All Modern Physics notes NDA Physics strategy

Why this matters

Five PYQs, a mix of EASY and MODERATE. The NDA tests the properties and uses of X-rays (and what they are NOT used for — radar), the charge carriers and I-V behaviour of semiconductors, and the names of scattering phenomena (Raman effect). Each is a one-fact or one-step question once you know the definitions.

Concept 1 of 4

X-rays — properties and uses

Intuition

X-rays are high-energy electromagnetic radiation with very short wavelengths (about 1 angstrom). They are produced by slamming high-speed electrons into a metal target. Their short wavelength lets them pass through soft tissue (medical imaging) and treat cancer, but they are NOT used for radar — radar uses long radio/microwaves.

Definition

X-rays are short-wavelength, high-energy electromagnetic waves:

Wavelength about $1\ \text{Å} = 10^{-10}$ m.
Produced by bombarding a metal target with high-energy electrons.
Uses: medical imaging (bone scans), cancer treatment (radiotherapy), security scanning, crystal structure study.
NOT used for radar — radar relies on long-wavelength radio/microwaves, not short X-ray wavelengths.
The dimensions of Planck's constant $h = E/f$ are those of angular momentum (J·s).

Statement about X-rays	True or false
Wavelength about 1 Å	True
Generated by bombarding a metal target with high-energy electrons	True
Used for radar systems because of their short wavelength	FALSE NDA 2023 — the false statement is that X-rays are used for radar. Radar uses long radio/microwaves, not X-rays.
Used to treat certain cancers	True

Everything about X-rays is true EXCEPT the radar claim. Radar = radio/microwave, not X-ray.

Practice this conceptself-check · 4 quick reps

From the bank · past-year question

Example 1Modern PhysicsMODERATE

Which one of the following statements about X-rays is not true?

[Q91 · Apr · 2023]

X-rays for radar is the WRONG statement

Radar needs long wavelengths that reflect off aircraft and ships — radio waves and microwaves. X-rays have wavelengths far too short for radar. Any option pairing X-rays with radar is false.

Concept 2 of 4

Dimensions of Planck's constant — same as angular momentum

Intuition

Planck's constant h links a photon's energy to its frequency through E = hf. Rearranging, h = E/f, which is energy divided by frequency — energy times time. Energy times time happens to be exactly the dimensions of angular momentum, so h carries the SI unit J·s.

Definition

From $E = hf$ , Planck's constant is $h = E/f$ :

Dimensionally, $[h] = \dfrac{[\text{energy}]}{[\text{frequency}]} = \dfrac{\text{J}}{\text{s}^{-1}} = \text{J}\cdot\text{s}$ .
J·s = (kg·m²/s²)·s = kg·m²/s = angular momentum (also the unit of action).
So $h$ has the same dimensions as angular momentum, not linear momentum or torque.

Dimensions of Planck's constant

[h] = \dfrac{[E]}{[f]} = \text{J}\cdot\text{s} = [\text{angular momentum}]

hPlanck's constant
Eenergy (J)
ffrequency (Hz = s⁻¹)

Worked example

The energy of a photon is E = hf. The dimensions of h are the same as those of which physical quantity?

Practice this conceptself-check · 4 quick reps

From the bank · past-year question

Example 2Modern PhysicsMODERATE

The energy E of a photon can be expressed as E = hf where f is the frequency and h is Planck's constant. The dimensions of h are the same as that of

[Q60 · Sep · 2025]

h is angular momentum, not linear momentum or torque

J·s = angular momentum. Linear momentum is kg·m/s; torque is N·m = J (no extra second). Only angular momentum (and action) matches J·s.

Concept 3 of 4

Semiconductors — p-type, n-type, and the I-V graph

Intuition

A pure semiconductor like silicon conducts a little. Doping it with impurities makes it n-type (extra electrons) or p-type (extra 'holes', i.e. missing electrons). A plain rectangular wafer of semiconductor still obeys Ohm's law — its current-voltage graph is a straight line through the origin. Charge carriers and the I-V shape are the two facts tested.

Definition

Semiconductor recall facts:

n-type: doped to have extra free electrons as the majority carriers.
p-type: doped to have extra holes (missing electrons, behaving as positive carriers) as the majority carriers.
A simple rectangular semiconductor wafer follows Ohm's law: its current-voltage (I-V) graph is a straight line through the origin (linear in both positive and negative quadrants).

Type	Majority charge carriers	Created by doping with
p-type	Holes (positive)	Trivalent impurity (e.g. boron)Q NDA 2017 — the majority charge carriers in a p-type semiconductor are holes.
n-type	Electrons (negative)	Pentavalent impurity (e.g. phosphorus)

p-type = holes (positive). n-type = electrons (negative). A plain wafer's I-V graph is a straight line through the origin.

Practice this conceptself-check · 4 quick reps

From the bank · past-year question

Example 3Modern PhysicsMODERATE

Which one of the following graphs correctly represents the current (I) – voltage (V) variation for a rectangular piece of a semiconductor wafer?

[Q59 · Sep · 2023]

p-type carriers are HOLES (positive), n-type are electrons

The letters track the carrier sign: p = positive (holes), n = negative (electrons). Distractors swap them. A plain wafer is still ohmic — linear I-V, not a diode curve.

Drill 1 more on semiconductors — p-type, n-type, and the i-v graph

Concept 4 of 4

Scattering phenomena — the Raman effect

Intuition

When light passes through a transparent substance, most of it scatters without changing colour (Rayleigh scattering). But a small part comes out with a SHIFTED frequency because it exchanged energy with the molecules — this frequency change is the Raman effect, discovered by C. V. Raman. The exam tests the name that matches 'scattered light with changed frequency'.

Definition

Named scattering phenomena:

Raman effect — when light is scattered by a molecule and its frequency CHANGES (energy exchanged with the molecule). Discovered by C. V. Raman (Nobel Prize 1930).
Rayleigh scattering — scattering WITHOUT a frequency change (makes the sky blue).
Do not confuse with the photoelectric effect (electron emission) or Rutherford scattering (alpha particles off nuclei).

Phenomenon	What happens
Raman effect	Scattered light's frequency CHANGES (inelastic scattering) NDA 2021 — light scattered with a changed frequency is the Raman effect.
Rayleigh scattering	Scattering with NO frequency change (elastic)
Photoelectric effect	Light ejects electrons from a metal — not scattering
Rutherford scattering	Alpha particles scatter off atomic nuclei

Frequency CHANGES = Raman. No change = Rayleigh. The other two are different phenomena entirely.

Practice this conceptself-check · 4 quick reps

From the bank · past-year question

Example 4Modern PhysicsMODERATE

When light is scattered by a molecule and the frequency of the scattered light is changed, this phenomenon is called

[Q80 · Apr · 2021]

Raman = frequency CHANGES; Rayleigh = no change

The defining feature of the Raman effect is a SHIFT in the scattered light's frequency. Rayleigh scattering leaves frequency unchanged. The wording "frequency is changed" points to Raman.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Dimensions of Planck's constant — same as angular momentum
Dimensions of Planck's constant
$[h] = \dfrac{[E]}{[f]} = \text{J}\cdot\text{s} = [\text{angular momentum}]$

Reference tables (3)

X-rays — properties and uses4 rows

Statement about X-rays	True or false
Wavelength about 1 Å	True
Generated by bombarding a metal target with high-energy electrons	True
Used for radar systems because of their short wavelength	FALSE NDA 2023 — the false statement is that X-rays are used for radar. Radar uses long radio/microwaves, not X-rays.
Used to treat certain cancers	True

Everything about X-rays is true EXCEPT the radar claim. Radar = radio/microwave, not X-ray.

Semiconductors — p-type, n-type, and the I-V graph2 rows

Type	Majority charge carriers	Created by doping with
p-type	Holes (positive)	Trivalent impurity (e.g. boron)Q NDA 2017 — the majority charge carriers in a p-type semiconductor are holes.
n-type	Electrons (negative)	Pentavalent impurity (e.g. phosphorus)

p-type = holes (positive). n-type = electrons (negative). A plain wafer's I-V graph is a straight line through the origin.

Scattering phenomena — the Raman effect4 rows

Phenomenon	What happens
Raman effect	Scattered light's frequency CHANGES (inelastic scattering) NDA 2021 — light scattered with a changed frequency is the Raman effect.
Rayleigh scattering	Scattering with NO frequency change (elastic)
Photoelectric effect	Light ejects electrons from a metal — not scattering
Rutherford scattering	Alpha particles scatter off atomic nuclei

Frequency CHANGES = Raman. No change = Rayleigh. The other two are different phenomena entirely.

Watch out for (4)

X-rays for radar is the WRONG statement
→ X-rays — properties and uses
h is angular momentum, not linear momentum or torque
→ Dimensions of Planck's constant — same as angular momentum
p-type carriers are HOLES (positive), n-type are electrons
→ Semiconductors — p-type, n-type, and the I-V graph
Raman = frequency CHANGES; Rayleigh = no change
→ Scattering phenomena — the Raman effect

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