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Quantum Physics Homework Help: Beta Decay

When a parent nucleus emits a β particle (i.e. an electron), mass number remains same because mass of electrons is negligibly low. Therefore, atomic number is increased by one. For example, according to help with homework experts when 90Th234 emits a β particle, the daughter nucleus has mass number = (234 – 0) = 234 and charge number = (90 + 1) = 91. This is called 91Pa234. The reaction can be represented as

90Th234 91Pa234 + -1e0 (β particle)

In general, we can write

ZXA Z+1YA + -1e0 + Q

Where Q is the energy of β particles, we now can find that

(i) Most of the β particles emitted carry small energies.

(ii) Only very few β particles carry maximum energy, called end point energy.

(iii) The energy spectrum of emitted β particles is continuous indicating, that the β particles can carry all possible energies from 0 to Qβ (max).

Further studies reveal that energy of nucleus emitting β particles decreases by an amount equal to the end point energy but most of the β particles emitted have energies smaller than the end point energy. Therefore, the principle of conservation energy is violet in β decay.

Again the principle of conservation of angular momentum is also violated in β decay. According to this is because β particle or electron has a spin = ½ (h/2∏). Therefore, in decay, spin of nucleus must change by ½ (h/2∏). But in actual practice, there is wither no change or an integral change in the spin of nucleus emitting β particle.

Neutrino hypothesis

The violations of the principles of conservation of energy and angular momentum were resolved by Pauli in the year 1931. He postulated that β decay is always accompanied by another particle of zero rest mass and zero charge. This particle was called neutrino (v). thus β decay of a nucleus may be represented as:

ZXA Z + 1YA + -1e0 + v + Q

The neutrino hypothesis implies that a low energy β particle is accompanied by a high energy neutrino and vice-versa. So the total energy Q of β particle and neutrino is constant and always equal to end point energy. Thus according to statistics homework answers experts the law of conservation of energy holds good in β decay.

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