“In a Bohr atom, the rate of increase of distance between consecutive orbits decreases as ‘n’increases.” Identify the statement to be True or False and give a mathematical explanation of yourresult
Question
“In a Bohr atom, the rate of increase of distance between consecutive orbits decreases as ‘n’increases.” Identify the statement to be True or False and give a mathematical explanation of yourresult
Solution
The statement is True.
In the Bohr model of an atom, the radius of the nth orbit is given by the formula:
r_n = n^2 * r_0
where r_0 is the radius of the first orbit (n=1), and n is the principal quantum number (the number of the orbit in question).
If we want to find the difference in radius (distance) between consecutive orbits, we can subtract the radius of the (n-1)th orbit from the nth orbit:
r_n - r_(n-1) = n^2 * r_0 - (n-1)^2 * r_0 = (n^2 - (n-1)^2) * r_0 = (2n-1) * r_0
This shows that the difference in radius between consecutive orbits increases linearly with n. However, the rate of increase (the derivative of the difference with respect to n) is constant (2*r_0), not increasing. Therefore, the rate of increase of distance between consecutive orbits does not decrease as n increases.
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