Atoms Test

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Atoms Test - 80

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Weekly Quiz Competition

Question 1
1 / -0

A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength $$980\mathring { A } .$$ The radius of the atom in excited state, in terms of Bohr radius a, will be:
$$\left( hc=12500\quad eV-\mathring { A } \right) $$

A
$$4{ a }_{ 0 }$$

B
$$16{ a }_{ 0 }$$

C
$$9{ a }_{ 0 }$$

D
None of these

Solution

Hint: Energy of photons = $$E=\frac{h c}{\lambda}$$
Solution:
Step 1: Find the energy of photon.
Given: $$h c=12500 \mathrm{eV}-A^{\circ}, \lambda=980 A^{\circ}$$
Energy of photons = $$E=\frac{h c}{\lambda}$$
$$\Rightarrow E=\frac{12500}{980}=12.75 \mathrm{eV}$$

Step 2: Find the excited state

Now, Energy of hydrogen atom in nth shell =$$E_{n}=\frac{-13.6}{n^{2}}$$
Energy absorbed by hydrogen atom = energy of photons
$$\Rightarrow E_{n}-E_{1}=E$$
$$\Rightarrow \frac{-13.6}{n^{2}}-\left[\frac{-13.6}{1^{2}}\right]=12.75 \mathrm{eV}$$
$$\Rightarrow 13.6-\frac{13.6}{n^{2}}=12.75$$
$$\Rightarrow 1-\frac{1}{n^{2}}=\frac{12.75}{13.6}$$
$$\Rightarrow 1-\frac{1}{n^{2}}=0.9375$$
$$\Rightarrow \frac{1}{n^{2}}=1-0.9375=0.0625$$

Step 3: Find radius in the excited state.
Radius of hydrogen atom = $$r=n^{2} a_{0}$$
$$\Rightarrow r=(4)^{2} a_{0}$$
$$\Rightarrow r=16 a_{0}$$
So, Radius of hydrogen atom in excited state is $$16 a_{0}$$
Question 2
1 / -0

The time taken by the electron in one complete revolution in the $$n^{th}$$ Bohr's orbit of the hydrogen atom is

A
Inversely proportional to $$n^2$$

B
Directly proportional to $$n^3$$

C
Directly proportional to $$\dfrac{h}{2\pi}$$

D
Inversely proportional to $$\dfrac{n}{h}$$

Solution
Question 3
1 / -0

The ratio of frequencies of the first line of the lyman series and the first line of blamer series is

A
$$\frac{{27}}{5}$$

B
$$\frac{{27}}{8}$$

C
$$\frac{8}{{27}}$$

D
$$\frac{4}{{27}}$$

Solution
Question 4
1 / -0

Hydrogen atoms in a sample are excited to $$n=5$$ state and it is found that photons of all possible wavelengths are present in the emission spectra. The minimum number of hydrogen atoms in the sample would be

A
$$5$$

B
$$6$$

C
$$10$$

D
$$infinite$$

Solution

The wavelengths present in emission spectra are shown in the figure.
Transitions $$a,e,h$$ and $$j$$ can be performed by a single atom also. This is also true about transitions $$b$$ and $$i$$, other transitions require one atom each.
Question 5
1 / -0

The radius of the orbital of electron in the hydrogen atom is $$ 0.5 A^0 $$ . the speed of the electron is $$ 2 \times 10^5 m/s $$. then, the current in the loop due to the motion of the electron is

A
1 mA

B
1.5 mA

C
2.5 mA

D
$$ 1.5 \times 10^{-2} m A $$

Solution
Question 6
1 / -0

Suppose, the electron in a hydrogen atom makes transition from $$n = 3$$ to $$n = 2$$ in $$10^{-8}$$s. The order of the torque acting on the electron in this period, using the relation between torque and angular momentum as discussed in the chapter on rotational mechanics is

A
$$10^{-34}$$ N m

B
$$10^{-24}$$ N m

C
$$10^{-42}$$ N m

D
$$10^{-8}$$ N m

Solution
Question 7
1 / -0

In an atom two electrons move round the nucleus in circular orbits of radii R and $$4R$$ respectively. The ratio of the time taken by them to complete one revolution is?

A
$$\dfrac{1}{4}$$

B
$$\dfrac{4}{1}$$

C
$$\dfrac{8}{1}$$

D
$$\dfrac{1}{8}$$

Solution
Question 8
1 / -0

The radius of the shortest orbit in a one-electron system is 18 pm. It may be

A
hydrogen

B
deuterium

C
$$He^+$$

D
$$Li^{++}$$

Solution
Question 9
1 / -0

In hydrogen atom, electron revolves around nucleus in circular orbit of radius $$5 \times 10 ^{- 11}\, m$$ at a speed $$2.2 \times 10^6 m/s$$. Then the orbital current will be:

A
3.2 mA

B
2.42 mA

C
1.12 mA

D
0.02 ma

Solution
Question 10
1 / -0

The minimum orbital angular momentum of the electron in a hydrogen atom is

A
$$h$$

B
$$h/2$$

C
$$h/2\pi$$

D
$$h/\lambda$$

Solution

According to Bohr's atomic theory, the orbital angular momentum of an electron is an integral multiple of $$\frac{h}{2π}$$.

$$\therefore L_n = \frac{nh}{2π}$$

Here,
n = Principal quantum number

The minimum value of n is 1.
So, the minimum value of the orbital angular momentum of the electron in a hydrogen atom is given by

$$L = \frac{h}{2π}$$