If an alpha particle were released from rest near the surface of a nucleus, what would its kinetic energy be when far away?
Answer to Problem 9P
Solution:
The kinetic energy of alpha particle when is far away from is 30 MeV.
Explanation of Solution
Given info:
Initially, the alpha particle was released from rest (= 0). Then, alpha particle is far away ()from nucleus. The atomic number ()of alpha particle is 2, and the mass number ()of alpha particle is 4. For nucleus its atomic number ()is 100 and its mass number ()is 257.
Formula used:
The conservation of total energy is defined as:
(1)
Where:
• , are respectively the initial and final potential energy.
• , are respectively the initial and final kinetic energy.
Calculation:
According to given info values:
(2)
And
(3)
Now, the initial potential energy ()is:
(4)
Inserting (2), (3)and (4)into equation (1)we have:
(5)
Where:
• is total charge of alpha particle, which can be obtained using:
(6)
Similarly, the charge for nucleus can be obtained using:
(7)
• is the distance between alpha particle and nucleus, which can be obtained using:
(8)
Now, inserting (6), (7)and (8)into equation (5)we have:
(9)
Where:
(10)
Chapter 30 Solutions
Physics: Principles with Applications
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