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Answer :
(a) The number of radon atoms will remain after 12 days is,
(b) The number of radon nuclei have decayed by this time will be,
Explanation :
<u>For part (a) :</u>
Half-life = 3.82 days
First we have to calculate the rate constant, we use the formula :
Now we have to calculate the number of radon atoms will remain after 12 days.
Expression for rate law for first order kinetics is given by:
where,
k = rate constant =
t = time passed by the sample = 12 days
a = initially number of radon atoms =
a - x = number of radon atoms left = ?
Now put all the given values in above equation, we get
Thus, the number of radon atoms will remain after 12 days is,
<u>For part (b) :</u>
Now we have to calculate the number of radon nuclei will have decayed by this time.
The number of radon nuclei have decayed = Initial number of radon atoms - Number of radon atoms left
The number of radon nuclei have decayed =
The number of radon nuclei have decayed =
Thus, the number of radon nuclei have decayed by this time will be,
Explanation:
It is given that,
Electric field,
We need to find the change in the electric potential energy of the proton-field system when the proton travels to x = 2.5 m
From the conservation of energy, the loss in potential energy is equal to the gain in kinetic energy and kinetic energy is is equal to the work done.
So, the change in electric potential energy of the proton field system is . Hence, this is the required solution.