The potential of an atom is given by V = V₀loge(r/r₀) where r₀ is a constant and r is the radius of the orbit. Assuming Bohr's model to be applicable, which variation or r_n with n is possible (n being a principal quantum number)?

$r_{n} \propto n$

$r_{n} \propto \frac{1}{n}$

$r_{n} \propto n^{2}$

$r_{n} \propto \frac{1}{n^{2}}$

Solution

$r_{n} \propto n$

Given that, V = V_olog_e (r/r_o)

Field,

$E = - \frac{dV}{dt} = - V_{o} (\frac{r}{r_{o}}) eE = \frac{{mV}^{2}}{r} or \frac{{eV}_{0} r_{0}}{r} = \frac{{mV}^{2}}{r} V = {(\frac{{eV}_{0} r_{0}}{m})}^{1 / 2} mV = (m_{e} V_{0} r_{0})^{1 / 2} = constant ∴ mvr = \frac{nh}{2 π}, Bohr' s quantum condition or r \propto n$

Some More Questions From Atoms Chapter

Four nuclei of an element undergo fusion to form a heavier nucleus, with the release of energy. Which of the two — the parent or the daughter nucleus — would have higher binding energy per nucleon?

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Atoms

Some More Questions From Atoms Chapter

Four nuclei of an element undergo fusion to form a heavier nucleus, with the release of energy. Which of the two — the parent or the daughter nucleus — would have higher binding energy per nucleon?

Which of the following transitions in hydrogen atoms emit photons of highest frequency?

The energy spectrum of β-particles [number N(E) as a function of β-energy E] emitted from a radioactive source is

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Atoms

The potential of an atom is given by V = V0loge(r/r0) where r0 is a constant and r is the radius of the orbit. Assuming Bohr's model to be applicable, which variation or rn with n is possible (n being a principal quantum number)? rn ∝ n rn ∝ 1n rn ∝ n2 rn ∝ 1n2

Some More Questions From Atoms Chapter

Four nuclei of an element undergo fusion to form a heavier nucleus, with the release of energy. Which of the two — the parent or the daughter nucleus — would have higher binding energy per nucleon?

Which of the following transitions in hydrogen atoms emit photons of highest frequency?

The energy spectrum of β-particles [number N(E) as a function of β-energy E] emitted from a radioactive source is

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation