Assertion : In Bohr model of hydrogen atom, the angular momentum of an electron in \( n \)th orbit is proportional to the square root of its orbit radius \( r_n \)
Reason (R): According to Bohr model, electron can jump to its nearest orbits only.
An assertion (A) and a reason (R) regarding Bohr's model of the hydrogen atom are provided. Both statements are analyzed:
This statement is false. Bohr's model dictates that the angular momentum (\(L\)) of an electron in the \(n\)-th orbit is quantized according to the equation:
\[ L = n \hbar \]
where:
The radius \(r_n\) of the \(n\)-th orbit is proportional to \(n^2\), such that:
\[ r_n \propto n^2 \]
Consequently, the angular momentum is directly proportional to \(n\), not to the square root of the radius. The assertion is thus incorrect.
This statement is true. Bohr's model explains that when an electron absorbs or emits energy, it transitions between orbits. However, these transitions are restricted to specific orbits corresponding to allowed energy levels. The electron can only move between these discrete orbits (energy levels) upon energy absorption or emission, typically to orbits with the closest energy values. Therefore, the reason is valid.
Although the reason (R) is correct, the assertion (A) is incorrect. Bohr's model establishes that angular momentum is proportional to \(n\), not to the square root of the radius. Therefore, the assertion is false, even though the reason is true.
The correct assessment is: Assertion is false, and Reason is true.
Assuming the experimental mass of \( {}^{12}_{6}\text{C} \) as 12 u, the mass defect of \( {}^{12}_{6}\text{C} \) atom is____MeV/\( c^2 \).
(Mass of proton = 1.00727 u, mass of neutron = 1.00866 u, 1 u = 931.5 MeV/\( c^2 \))
The binding energy per nucleon of \(^{209} \text{Bi}\) is _______ MeV. \[ \text{Take } m(^{209} \text{Bi}) = 208.98038 \, \text{u}, \, m_p = 1.007825 \, \text{u}, \, m_n = 1.008665 \, \text{u}, \, 1 \, \text{u} = 931 \, \text{MeV}/c^2. \]