Atoms Test - 78...

The electric potential between a proton and an electron is given by $V=VIn\dfrac { r }{ { r }_{ 0 } }$, where ${ r }_{ 0 }$ is a constant. Assuming Bohr's model to be applicable,write variation of ${ r }_{ n}$ with $n,\ n$ being the principal quantum number.

Mean free path of gas molecule at constant temperature is inversely proportional to 

The photon radiated from hydrogen corresponding to $2nd$ line of Lyman series is absorbed by a hydrogen like atom $'X'$ in $2nd$ excited state. As a result the hydrogen like atom $'X'$ makes a transition to $n^{th}$ orbit. Then,

The de Broglie wavelength of an electron in $n^{th}$ Bohr orbit of radius $a_n(a_0$ being the first orbit radius$)$:

Let $F _ { 1 }$ be the frequency of second line of Lyman series and $F _ { 2 }$ be the frequency of first-line ofBatmer series then frequency of first line of Lyman series is given by

If $\lambda_{max.} = 6563 \dot{A}$ , then wavelength of second line for Balmer series will be :

The magnetic field at the center of a hydrogen atom due to the motion of electron varies with the principal quantum number as

The wavelength of second line of Balmer series is 4815 $\mathring A$. The wavelength of first line Balmer series in the same atom is 

According to DE Broglie, wavelength of electron in second orbit is 10$^{ -9 }$ meter. Then the circumstances of orbit is :-

Imagine an atom made of a proton and a hypothetical particle of double the mass as that of an electron but the same charge. Apply Bohr theory to consider transitions of the hypothetical particle to the ground state . Then, the longest wavelength (in terms of Rydberge constant for hydrogen atom ) is