Scattering Angle vs Number of Alpha Particles Graph
Physics · Atoms · NEET
In the Geiger-Marsden experiment, the number of scattered alpha particles N is very large for small scattering angles and falls off very steeply as the angle theta increases. Only a very tiny number reach large angles like 90 degrees or more. Memory hook: "Small angle = big crowd, large angle = almost empty." The math behind the curve is N proportional to 1 / sin^4(theta/2).
The N vs theta curve starts very high at small angles and drops steeply as theta increases, following N proportional to 1/sin^4(theta/2). The small non-zero tail at large angles proves the nucleus is tiny and dense.
Your doubts, answered
Why is N largest at small scattering angles?
Most alpha particles pass far from the tiny nucleus. A far pass means only a small sideways push, so a small deflection angle. Because the atom is mostly empty space, far-passing particles are the majority. So the count N is huge for small theta and the graph starts very high on the left.
Why does the graph fall so steeply, not gently?
The count follows N proportional to 1 / sin^4(theta/2). The fourth power makes it drop extremely fast. For example, going from 60 degrees to 120 degrees the value of sin^4(theta/2) changes a lot, so N drops many times over. That is why the curve plunges, it is not a gentle slope.
Is the graph a straight line?
No. It is a sharply falling curve. N is very high at small angles and hugs the axis at large angles. Students who draw a straight downward line lose marks. The correct shape is a steep decay curve, like a slide that drops fast then flattens near zero.
What does the graph prove about the atom?
That a very small number of particles bounce back at large angles proves the positive charge and mass are packed in a tiny nucleus at the centre. If charge were spread out (Thomson model), no particle could turn through a large angle, so the tail of the graph at big theta would be exactly zero.
Does N ever become exactly zero?
No, N stays very small but non-zero even up to 180 degrees. A few head-on or near head-on approaches send particles almost straight back. The graph gets extremely close to the theta axis but never actually touches zero for finite angles.
⚠️ The NEET trap ✗ The number of scattered alpha particles increases as the scattering angle increases. ✓ The number is maximum at small angles and decreases steeply as the angle increases, following N proportional to 1/sin^4(theta/2). 🧠 Read the graph left to right: it starts HIGH and falls. If your chosen option rises with theta, it is wrong.
Real NEET questions
Re-NEET 2026
In the Geiger-Marsden experiment, the number of scattered alpha-particles N(theta) is plotted as a function of scattering angle theta. Which option represents the correct plot?
A · N(theta) increasing with theta
B · A broad maximum near theta approx 60 degrees
C · N(theta) very large at small theta and falling steeply as theta increases ✓
D · A symmetric peak centred at theta approx 90 degrees
Solution: Rutherford's scattering formula gives N(theta) proportional to 1 / sin^4(theta/2). Step 1: as theta approaches 0, sin(theta/2) approaches 0, so N becomes very large; most particles scatter through tiny angles. Step 2: as theta increases, sin^4(theta/2) grows quickly, so N falls very steeply. Step 3: only a few particles reach large angles. This matches a curve that is very high at small theta and drops sharply, which is option (C).
Solved Atoms NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the formula for the alpha scattering distribution?
N(theta) is proportional to 1 / sin^4(theta/2), where theta is the scattering angle. This is Rutherford's scattering formula.
At which angle is N maximum?
N is maximum at the smallest angles, near theta = 0. The graph is highest on the left and falls as theta grows.
Why do a few particles scatter at large angles?
A small number pass very close to the tiny dense nucleus and feel a strong repulsion, so they deflect through large angles. This is why the graph has a small but non-zero tail at big theta.
What does the steep fall tell us about the atom?
It tells us the positive charge and mass sit in a very small central nucleus, confirming Rutherford's nuclear model over Thomson's spread-out model.
Is N versus theta a linear graph?
No, it is a steeply decaying curve because of the fourth-power sine term, not a straight line.
