Imagine an atom made up of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has wavelength λ (given in terms of the Rydberg constant R for the hydrogen atom) equal to

(1) 9/(5R)                 
(2) 36/(5R)
(3) 18/(5R)               
(4) 4/R

Subtopic:  Bohr's Model of Atom |
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In the Bohr model of the hydrogen atom, let R, v and E represent the radius of the orbit, the speed of electron and the total energy of the electron respectively. Which of the following quantity is proportional to the quantum number n ?

(1) R/E               

(2) E/v

(3) RE               

(4) vR

Subtopic:  Bohr's Model of Atom |
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The electric potential between a proton and an electron is given by \(V = V_0\mathrm{Ln}\left(\frac{r}{r_0}\right)\) where \(r_0\) is a constant. Assuming Bohr’s model to be applicable, the variation of \(r_n\) with \(n\), \(n\) being the principal quantum number, is:
1. \(r_n \propto n\)
2. \(r_n \propto\frac{1}{n}\)
3. \(r_n\propto n^2\)
4. \(r_n \propto\frac{1}{n^2}\)

Subtopic:  Bohr's Model of Atom |
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If the atom Fm100257 follows the Bohr model and the radius of Fm100257 is n times the Bohr radius, then the value of n is:

(1) 100               
(2) 200
(3) 4                   
(4) 14

Subtopic:  Bohr's Model of Atom |
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Consider a hydrogen like atom whose energy in nth exicited state is given by En=-13.6 Z2n2 when this excited atom makes a transition from excited state to ground state, most energetic photons have energy Emax = 52.224 eV and least energetic photons have energy Emin = 1.224 eV. The atomic number of atom is
(a) 2                 (b) 5
(c) 4                 (d) None of these

Subtopic:  Bohr's Model of Atom |
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When a hydrogen atom is excited from ground state to first excited state then the incorrect option is– 

1. its kinetic energy increases by 10.2 eV 

2. its kinetic energy decreases by 10.2 eV 

3. its potential energy increases by 20.4 eV 

4. its angular momentum increases by 1.05 × 1034 J-s

Subtopic:  Bohr's Model of Atom |
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The ionisation potential of H-atom is  13.6 V. When it is excited from ground state by monochromatic radiations of 970.6 A0, the number of emission lines will be (according to Bohr’s theory) 
(1) 10           

(2) 8

(3) 6             

(4) 4

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A double charged lithium atom is equivalent to hydrogen whose atomic number is 3. The wavelength of required radiation for exciting electron from first to third Bohr orbit in Li++ will be (Ionisation energy of hydrogen atom is 13.6eV) 
(a) 182.51 Å                 (b) 177.17 Å
(c) 142.25 Å                 (d) 113.74 Å

Subtopic:  Bohr's Model of Atom |
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In a hypothetical Bohr hydrogen, the mass of the electron is doubled. What will be the energy \(E_0\) and the radius \(r_0\) of the first orbit?
\((a_0\) is the Bohr radius) 
1. \(E_0=-27.2 ~\text{eV};~r_0={a}_0 / 2\)
2. \(E_0=-27.2 ~\text{eV}; ~r_0={a}_0\)
3. \(E_0=-13.6~\text{eV} ; ~r_0={a}_0 / 2\)
4. \(E_0=-13.6 ~\text{eV}; ~r_0={a}_0\)

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The ratio of the speed of the electrons in the ground state of hydrogen to the speed of light in vacuum is

1. 1/2                2. 2/137
3. 1/137            4. 1/237

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