Three particles having charges in the ratio of 2 : 3 : 5 produce the same point on the photographic film in Thomson experiment. Their masses are in the ratio of 3 : 5 : 2

As the three charges produce the same spot on the photographic film, they must have the same value of specific charge. Specific charge is defined as charge/mass. Let the charges be 2k, 3k, and 5k, and the masses be 3m, 5m, and 2m respectively. Then the specific charges are:

Particle 1: (2k)/(3m)
Particle 2: (3k)/(5m)
Particle 3: (5k)/(2m)

Since they produce the same spot, their specific charges must be equal:

(2k)/(3m) = (3k)/(5m) = (5k)/(2m)

Let's consider the first two ratios:

(2k)/(3m) = (3k)/(5m)
10km = 9km
This equation is only true if k=0 or m=0. This is not physically possible. Therefore, there must be a different mass ratio.

Let's assume the ratio of masses is a:b:c and solve using the specific charge concept:
(2k)/(am)=(3k)/(bm)=(5k)/(cm)
We must have:
2k/a = 3k/b = 5k/c
This gives us 2/a = 3/b = 5/c
We can choose a=2, b=3, and c=5. Thus the ratio of masses is 2:3:5