Concept explainers
(a)
Identify the unknown product in the reaction of
(a)
Answer to Problem 87P
The unknown product in the reaction of
Explanation of Solution
The given reaction iss
Here,
Conservation of nucleon number: The number of nucleon number in reactant is equal to the number of nucleon number in the product of the reaction. Therefore,
Conservation of charge: The number of protons in reactant is equal to the number of protons in the product of the reaction. Therefore,
In periodic table, the element with atomic number
(b)
The distance between the centers of alpha particle and nitrogen nucleus when they are just touching.
(b)
Answer to Problem 87P
The distance between the centers of alpha particle and nitrogen nucleus when they are just touching is
Explanation of Solution
The mass of number of
Write the equation for radius
Here,
The radius of
The radius of
Therefore, the distance between the centers of alpha particle and nitrogen nucleus when they are just touching is
(c)
The minimum value of the kinetic energy of the alpha particle and nitrogen nucleus necessary to bring them into contact.
(c)
Answer to Problem 87P
The minimum value of the kinetic energy of the alpha particle and nitrogen nucleus necessary to bring them into contact is
Explanation of Solution
The distance between the centers of proton and nitrogen nucleus when they just touching is
Write the formula for electric potential energy
Here,
Substitute
Therefore, the minimum value of the kinetic energy of the alpha particle and nitrogen nucleus necessary to bring them into contact is
(d)
Whether the total kinetic energy of the reaction products more or less than the kinetic energy in part (c). And calculate the kinetic energy difference.
(d)
Answer to Problem 87P
The total kinetic energy of the reaction products is less than the initial kinetic energy of the reactants. And the difference in their kinetic energy is
Explanation of Solution
The
Write the formula for energy
Here,
The mass difference between the product and the reactant of the overall equation is
The mass difference is positive, the mass of the product is greater than the mass of the reactant. Therefore the kinetic energy of the product is less than the kinetic energy of the reactant.
Substitute
Thus, the difference in their kinetic energy is
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