HALF LIFE and BINDING ENERGY

[loreben]

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Hi Sdners,
I have tried solving this question but am not getting the accurate answer. I was wondering if anyone could please walk me through this problem. Thank you 🙂.

Question 1
A system consists of No radioactive nuceli at time t=0. The number of nucei remaining after a half life is?
(a) 1/4No
(b) 3/4No
(c) 1/sqrt(2) No

Question 2

Calculate the binding energy of an alpha particle.

 

[GyroGyro]

For question 2, what you have to do is is add up the mass of the individual protons and neutrons within an alpha particle (which should be > 4 because it consists of 2 protons and 2 neutrons and the individual particles should always sum up to be greater than the mass of the entire particle) and then subtract 4 from this number (the mass number of the alpha particle).

The way you get the "m" in E = mc^2 (E is the binding energy, c is the speed of light) is from finding the difference in the mass of the individual particles summed up (2 protons and 2 neutrons) and then subtracting the mass number of the entire particle (in this case, 4 for the alpha particle).

As for question one, is the answer not just 1/2 No? I mean it seems that after one half life, you would lose half your material.

 

[loreben]

Thanks for your response. As for the first question i thought 1/2No would be the right answer as well but it isn't.

 

[indianjatt]

Thanks for your response. As for the first question i thought 1/2No would be the right answer as well but it isn't.

Agree with the above poster for #2. Are you sure that there isn't more information for the first question? Maybe they say how much is left after 2 half lives or t = 5, etc?

 

[MD Odyssey]

Calculate the binding energy of an alpha particle.

No additional information is needed here.

Binding energy is the energy stored in the electric field by the assembly of the nucleus. Textbooks notwithstanding, energy can be converted into matter and vice versa. Since the total sum of the two is a constant for all systems, the binding energy is find by simply determining the difference between the mass of an alpha particle and that of its constituent parts, namely two protons and two neutrons.

If you add up the mass of two protons and two neutrons, you'll get 4.03188 u. But, the mass of an alpha particle is 4.00153 u, so there is a discrepancy here of 0.03035 u. That mass is the matter which has been converted into energy. The binding energy is therefore given by the familiar equation:

which you crank out for yourself, work through the units, and when you're finished you get a binding energy of about 28 MeV.

 

[loreben]

Thanks guys for helping me out with the binding energy question and i understand it now.

It's the half life question am having problems with especially since the answer is said to be 1/sqrt 2.

Thanks.

 

[MT Headed]

Either there is a mistake in the question or a mistake in the answer. Can you check the question again? Maybe it said "The number of nuclei remaining after half a half life is?"

 

[loreben]

Sorry Guys, i made a typo while i was composing the question. The edited question is below:

A system consists of No radioactive nuceli at time t=0. The number of nuceli remaining after half a half life (that is, at time t=1/2[T1/2] ) is:

(a)1/4No
(b)3/4No
(c)1/sqrt(2No)

 

[MT Headed]

You didn't make it clear if you still needed a walk through, but here I go:

after 1 half life, you have (1/2) remaining
after 2 half lives, you have (1/4), or (1/2)^2 remaining
in general, after N half lives, you have (1/2)^N remaining

So... plug in N=(1/2)

The answer you seek is the sqrt(1/2), or 1/sqrt(2).