Atoms Test

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Atoms Test - 75

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Weekly Quiz Competition

Question 1
1 / -0

Let the potential energy of a hydrogen atom in the ground state be zero. Then, its energy in the first excited state will be

A
23.8 eV

B
27.2 eV

C
10.2 eV

D
13.6 eV

Solution
Question 2
1 / -0

If the ionisation energy of a hydrogen like Bohr atom is 4 Rydberg, then the wavelengths of radiation emitted when the electron jumps from first excited state to the ground state and the radius of the first orbit of this atom are:

A
$$3.04 \overset { \circ }{ A } ,0.53 \overset { \circ }{ A } $$

B
$$304 \overset { \circ }{ A } , 0.265 \overset { \circ }{ A } $$

C
$$912 \overset { \circ }{ A } , 0.53 \overset { \circ }{ A } $$

D
$$3.04 \overset { \circ }{ A } , 0.265 \overset { \circ }{ A } $$

Solution

$$\begin{array}{l}\text { Ionisation energy, } E=R z^{2}\\\qquad\begin{aligned}Rz^{2} &=4 R \\z &=2\end{aligned}\end{array}$$

$$\text { Radius of 1st orbit is } \dfrac{0.529}{2}A^{0}\text{=0.265} A^{0}$$

$$\begin{array}{l}\text { wavelength } \\\qquad \dfrac{1}{\lambda}=R z^{2}\left[\dfrac{1}{n_{1}^{2}}-\dfrac{1}{n_{2}^{2}}\right]\end{array}$$

$$\begin{array}{ll}n_{1}=1 & n_{2}=2 \\\text { we get, } & \lambda=304 A^{0}\end{array}$$
Question 3
1 / -0

The ratio of areas within the electron orbits for the first excited state to the ground state for hydrogen atom is

A
$$16:1$$

B
$$18:1$$

C
$$4:1$$

D
$$2:1$$

Solution

The square radius of the orbit is directly proportional to the power of four of the number of state.
$$r^2 \alpha$$ $$n^4$$
Where, n is the number of state
Areas of hydrogen for excited state
$$A_1$$ $$\alpha$$ $$n_1^4$$
Here, n = 2 for excited state
The area of hydrogen for the ground state
$$A_0$$ $$\alpha$$ $$n_0^4$$
Here, n = 1 for ground state
Now, the ratio of areas between the electron orbits for the first excited state to the ground state for the hydrogen atom is
$$\frac{A_1}{A_0} = (\frac{n_1}{n_0})^4$$
$$\frac{A_1}{A_0} = (\frac{2}{1})^4$$
$$\frac{A_1}{A_0} = (\frac{16}{1})$$
Hence, The ratio of the area is $$16:1$$.
Question 4
1 / -0

The innermost orbit of the hydrogen atom has a diameter of $$1.06 A^o$$. What is the diameter of the tenth orbit?

A
$$5.3 A^o$$

B
$$10.6 A^o$$

C
$$53 A^o$$

D
$$106 A^o$$

Solution
Question 5
1 / -0

Find an expression for de Broglie wavelength for an electron in the $$n^{th}$$ orbit of the Bohr model of the hydrogen atom and hence find its value when the electron is in n = 4 level.
Take radius of nth orbital of Bohr's model of H-atom; $$r_n = (53 \ n^2) $$ pm

A
1.33 nm

B
1.20 nm

C
1.50 nm

D
None

Solution
Question 6
1 / -0

A satellite of mass $$10\ kg$$ orbites around the earth once every $$2\ h$$ in an orbit of radius $$8000\ km$$. If Bohr's angular momentum is assumed to be applicable to the satellite, the quantum number of the orbit of the satellite is

A
$$6.4\times 10^{37}$$

B
$$5.3\times 10^{45}$$

C
$$4.9\times 10^{46}$$

D
$$6.9\times 10^{42}$$

Solution
Question 7
1 / -0

According to Bohr modal, magnetic field at the centre (at the nucleus) of a hydrogen atom due to the motion of electron in $$n^{th}$$ orbit is proportional to:

A
$$1/n^3$$

B
$$n^3$$

C
$$n^5$$

D
1/$$n^5$$

Solution
Question 8
1 / -0

The $$H_{a}$$-line of hydrogen

A
has a wavelength 4860 $$\overset {0}{A}$$

B
has a wavelength 6562$$\overset {0}{A}$$

C
has a wavelength smaller then that of the $$H_{\beta}$$-line

D
is emitted in the transition from the second excited state of the first excited state

Solution
Question 9
1 / -0

The wave number of first line in Balmer series of hydrogen spectrum is (Rydberg constant, $$R_H = 109,687 \,cm^{-1}$$) nearly

A
$$82,259 \,cm^{-1}$$

B
$$152,00 \,cm^{-1}$$

C
$$97,492 \,cm^{-1}$$

D
$$15,200 \,cm^{-1}$$

Solution

$$\begin{array}{l}\text { Wave number } \\\text { Here, }\quad\left[\bar{v}=R_{H} z^{2}\left[\frac{1}{n_{i}{ }^{2}}-\frac{1}{n_{2}^{2}}\right]\right. \\R_{H}=109687 \\z=1\end{array}$$

$$ \begin{aligned}\text { Balmar } n_{1}=2 \text { , and } n_{2}=3\\\bar{v}=109687\left[\frac{1}{(2)^{2}}-\frac{1}{(3)^{2}}\right]\\\bar{v}=109687\left[\frac{1}{4}-\frac{1}{9}\right]\end{aligned}$$

$$\bar{v}=15200 \mathrm{~cm}^{-1}$$
Question 10
1 / -0

Which of the following is inversely proportional to the square of principal quantum number in Bohr's atomic model?

A
Total energy of the electron in $$n^{th}$$ orbit.

B
Radius of the $$n^{th}$$ orbit.

C
Frequency of revolution in $$n^{th}$$ orbit.

D
Time period of revolution in $$n^{th}$$ orbit.

Solution