# Simple Atomic Mass Unit question

## Homework Statement

The uranium isotope 235U captures a neutron and undergoes fission to produce 93Rb and 141Cs. Calculate the energy released in this process.

The nuclear masses of the relevant isotopes are
235U 235.0439u,
93Rb 92.9217u,
141Cs 140.9195u

## The Attempt at a Solution

n + 235U → 93Rb + 141Cs + 2n

LHS 235.0439 + 1.0087
RHS 92.921712 + 140.91949 + 2.10087

Difference is 0.1943u = 181 MeV

I realise the quantity of 1.0087 is the mass of neutron divided by one unified atomic mass unit. So that's (1.67493 x 10^-27) / (1.66 x 10^-27).
Also, the 2.10087 number is simply double this.

How have the 235.0439, 92.921712 & 140.91949 values been calculated? I know it's to do with E=Mc^2

Thank you.

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It all has to do with the mass difference, (mass before) - (mass after) = (released) or (consumed energy). The values for the nuclei´s masses has to be taken from a table. There is no way of calculating the mass of a nuclei, it has to be measured.

Can it not be calculated from the part of the question which states;

The nuclear masses of the relevant isotopes are
235U 235.0439u,
93Rb 92.9217u,
141Cs 140.9195u

The difference in mass is what is relevant, ((Mass before)-(Mass after)).*c^2 = E. To calculate this you also need the mass of the neutron. The mass of the neutron can not be calculated and needs to be taken from a table. Also in order to get the mass in kilograms for the other nuclei you simply multiply it with the atomic mass unit, just as with the neutron.

In the answer, how is it known that 2n should be added? Why 2?

Borek
Mentor
In the answer, how is it known that 2n should be added? Why 2?
Take a look at the reaction - how many neutrons are produced?

Is it because the total nucleon number on both sides must equal. Since LHS=236 RHS can only equal this by adding 2n.