Validating the Bohr's Model

Q. Using Rydberg's Formula find out what is dependency of wavelength of a photon emitted on the atomic number of a hydrogen like atom. (Assuming all other parameters of the equation to be constant)

1. Higher is the atomic number, more is the wavelength
2. Higher is the atomic number, less is the wavelength
3. Can't be answered using Rydberg's Formula
4. Wavelength is independent of the atomic number

Q.

In which of the following systems will the wavelength corresponding to n = 2 to n = 1 be minimum?

1. Singly ionized helium

2. Doubly ionized lithium

3. Hydrogen atom

4. Deuterium atom

Q.

The above picture depicts the possible transitions of electron in Bohr's atomic model.
Match the transition lines to corresponding series.
$\begin{array}{cc}\text{p.}{L}_1& \text{i. Lyman}\\ \text{q.}{L}_2& \text{ii. Blamer}\\ \text{r.}{L}_3& \text{iii. Paschen}\\ \text{s.}{L}_4& \text{iv. None of these}\end{array}$

1. p-ii ; q-iii ; r-i ; s-iv

2. p-iii; q-i; r-ii; s-iv

3. p-i ; q-I ; r-ii ; s-iii

4. p-iv; q-ii; r-i; s-iii

Q. Suppose an electron is attracted towards the originby a force $\frac{k}{r}$ where 'k' is a constant and 'r' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the $n^{th}$ orbital of the electrons is found to be '$r_n$' and the kinetic energy of the electron to be '$T_n$'. Then which of the following is true?

1. $T_n\propto \frac{1}{n^2},r_n\propto n^2$
2. $T_n$ independent of n, $r_n\propto n$
3. $T_n\propto \frac{1}{n},r_n\propto n$
4. $T_n\propto \frac{1}{n},r_n\propto n^2$

Q.

Suppose in an imaginary world the angular momentum is quantized to be even intergral multiples of $\frac{h}{2\pi }$. What is the longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model ?

Q.

A hydrogen atom emits ultraviolet radition of wavelen gth 102.5 nm. What are the quantum numbers of the states involved in the transition ?

Q. Draw a neat labelled energy level diagram and explain the different series of spectral lines for hydrogen atom.

Q. In which of the following translations will the wavelength be minimum ?

1. n - 5 to n -4
2. n - 4 to n - 3
3. n - 3 to n - 2
4. n - 2 to n - 1

Q. The wavelength of the emitted radiation, if electron in hydrogen atom jumps from the third orbit to second orbit is

1. $\lambda =\frac{36}{5R}$
2. $\lambda =\frac{5R}{36}$
3. $\lambda =\frac{5}{R}$
4. $\lambda =\frac{R}{6}$

Q. The wavelength of the first line in balmer series in the hydrogen spectrum is $\lambda$. What is the wavelength of the second line :

1. $\frac{20\lambda }{27}$
2. $\frac{5\lambda }{36}$
3. $\frac{3\lambda }{16}$
4. $\frac{3\lambda }{4}$