Question

In Rutherford
scattering experiment the number of Alpha particle scatter at angle theta is equal to 60 degree is 12 per minute the number of Alpha particles per minute when scatter at the angle of 90 degree​

Answer 1

Answer:

According to Rutherford's scattering experiment we know the relation.

N(θ) is directly proportional to Z^2/sin^4(θ/2).

In which N(θ) is the number of alpha particles scattered through an angle of θ.

For 1st case:  N(θ)=12 and θ=60.

So, 12 = k*Z^2/sin^4(60/2).                          (1)

12 = k*Z^2/sin^4(30).

For the 2nd case θ=90.

So, N(θ) = k*Z^2/sin^4(90/2).                       (2)

Now dividing equation 1/2 we will get.

12/N(θ) = k*Z^2/sin^4(30) / k*Z^2/sin^4(90/2).

or, 12/N = (1/√2)⁴/(1/2)⁴ = (√2)⁴  

or, N = 3. which is the total number of alpha particles scattered through an angle of 90.

Answer 2

according to Rutherford scattering experiment, $N(\theta)\propto\frac{Z^2}{sin^4\left(\frac{\theta}{2}\right)}$

where $N(\theta)$ denotes number of alpha - particle scattered through an angle of θ .

case1: N(θ) = 12, (θ) = 60°

so, $12=k\frac{Z^2}{sin^4(30^{\circ})}$

case2 : (θ) =90°

so, $N(\theta)=k\frac{Z^2}{sin^4(45^{\circ})}$

from case 1 and 2 ,

$\frac{12}{N(\theta)}=\frac{sin^4(45)}{sin^4(30)}$

or, 12/N = (1/√2)⁴/(1/2)⁴ = (√2)⁴

or, N = 3

hence, number of alpha particles scattered through an angle of 90° per minute by the same nucleus is 3