Bohr's Model

According to the Bohr Theory, among the following, which transition in the hydrogen atom will give rise to the least energetic photon?

The energy of the second Bohr orbit of the hydrogen atom is $-328 \mathrm{kJ} {\mathrm{mol}}^{-1}$. Hence, the energy of the fourth Bohr orbit would be

The Bohr orbit radius for the hydrogen atom (n = 1) is approximately  $0.530\AA .$  The radius for the first excited state (n = 2) orbit is  $(in\AA )$

The radius of hydrogen atom in the ground state is  $0.53\mathrm{\AA }.$  The radius of  ${\mathrm{Li}}^{2+}$ ion (Atomic number = $3$) in first orbit is

An electron revolving round in an orbit has angular momentum equal to $\frac{\mathrm{h}}{2\mathrm{\pi }}$. Can it lose energy? 

On what basis did Bohr assume the concept of stationary orbits for an electron? 

Define angular momentum. In the relation $\mathrm{mvr}=\frac{\mathrm{nh}}{2\mathrm{\pi }}$, what do $\mathrm{m},\mathrm{v},\mathrm{r}$ and $\mathrm{h}$ denote? 

One electron is made to revolve around a proton and it possesses the least possible energy and another electron is made to revolve around an $\mathrm{\alpha }-$particle with the same energy. Calculate the ratio of the distances of the electrons from the respective species.

An electron is present in a hydrogen atom in the ground state and another electron is present in a single electron species of beryllium. In both the species the distance between the nucleus and electron is same. Calculate the difference in their energies.

What is the amount of energy needed to remove an electron from a hydrogen atom to produce a ${\mathrm{H}}^{+}$ ion? Explain. 

'Electrons jump from one orbit to another orbit.' Justify this statement on the basis of Bohr’s theory. 

Bohr's theory can explain the spectra of multielectron species.

Give an equation to calculate the following: 

The energy of the nth orbit of a hydrogen atom. 

Give an equation to calculate the following: 

The radius of the nth orbit of hydrogen atom. 

Calculate the ratio of radius of ${\mathrm{Li}}^{+2}$ ion in $3^{\mathrm{rd}}$ energy level to that of ${\mathrm{He}}^{+}$ ion in $2^{\mathrm{nd}}$ energy level.

For ${\mathrm{He}}^{+}$, a transition takes place from the orbit of radius $105.8\mathrm{pm}$ to the orbit of radius $26.45\mathrm{pm}$. The wavelength (in $\mathrm{nm}$ ) of the emitted photon during the transition is

Bohr radius, $\mathrm{a}=52.9 \mathrm{pm}$
Rydberg constant, ${\mathrm{R}}_{\mathrm{H}}=2.2\times {10}^{-18} \mathrm{J}$
Planck's constant, $\mathrm{h}=6.6\times {10}^{-34}\mathrm{Js}$
Speed of light, $\mathrm{c}=3\times {10}^8 {\mathrm{ms}}^{-1}$ ]

In Bohr's model of hydrogen atom, the radius of the first electron orbit is $0.53{\mathrm{A}}^{\mathrm{o}}$. What will be the radius of the third orbit? 

The energy of an electron in the first Bohr orbit of hydrogen atom is $-2.18\times {10}^{-18} \mathrm{J}$ Its energy in the third Bohr orbit is$\_\_\_\_\_\_\_.$