Physics Class 12 NCERT Solutions: Chapter 13 Nuclei Part 10 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Binding Energy of Nucleus

Q: 25. A source contains two phosphorous radio nuclides and . Initially, of the decays come from . How long one must wait until do so?

Answer:

Half-life of days

Half-life of , days

Nucleus decay is 10 % of the total amount of decay.

The source has initially of nucleus and 90 % of nucleus.

Suppose after days, the source has of nucleus and 90 % of nucleus.

Initially:

Number of nucleus

Number of nucleus

Finally:

Number of nucleus

Number of nucleus

For nucleus, we can write the number ratio as:

For , we can write the number ratio as:

On dividing equation (1) by equation (2) , we get:

It will take about 208.5 days for 90 % decay of .

Q: 26. Under certain circumstances, a nucleus can decay by emitting a particle more massive than an particle. Consider the following decay processes:

Calculate the Q-values for these decays and determine that both are energetically allowed.

Answer:

Take a emission nuclear reaction:

We know that:

Mass of

Mass of

Mass of

Hence, the Q-value of the reaction is given as:

But

Hence, the Q-value of the nuclear reaction is . Since the value is positive, the reaction is energetically allowed.

Now take a emission nuclear reaction:

We know that:

Mass of ,

Mass of

Mass of

Q-value of this nuclear reaction is given as:

Hence, the Q value of the second nuclear reaction is . Since the value is positive, the reaction is energetically allowed.