Atoms Test

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Atoms Test - 42

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Weekly Quiz Competition

Question 1
1 / -0

The nuclear radius of $$_{ 4 }^{ }{ { Be }^{ 8 } }$$ nucleus is :

A
$$1.3\times { 10 }^{ -15 }m$$

B
$$2.6\times { 10 }^{ -15 }m$$

C
$$1.3\times { 10 }^{ -13 }m$$

D
$$2.6\times { 10 }^{ -13 }m$$

Solution

Mass number of $$_4Be^8$$ $$A = 8$$
Nuclear radius, $$R = R_o A^{1/3}$$ where $$R_o = 1.3 \times 10^{-15} m$$
$$\therefore$$ $$R = 1.3\times 10^{-15} \times 8^{1/3}$$ $$m$$
$$\implies$$ $$R = 1.3\times 10^{-15} \times 2 = 2.6\times 10^{-15} m$$
Question 2
1 / -0

The characteristic spectrum of an atom is observed as

A
Pure line spectrum

B
Emission band spectrum

C
Absorption line spectrum

D
Absorption band spectrum

Solution

When atoms are excited they emit light of certain wavelengths which correspond to different colors and the emitted light is observed as a series of colored lines with dark spaces in between. The series of colored lines are called a line or atomic spectra. Each element produces a unique set of spectral lines and since no two elements emit the same spectral lines, elements can be identified by their line spectrum.
Question 3
1 / -0

The cathode rays are

A
A stream of electrons

B
A stream of positive ions

C
A stream of uncharged particles

D
The same as canal rays

Solution

A cathode ray is a beam of electrons in a vacuum tube traveling from the negatively charged electrode (cathode) at one end to the positively charged electrode (anode) at the other, across a voltage difference between the electrodes. They are also called electron beams.
Question 4
1 / -0

Atomic spectrum should be :

A
Pure line spectrum

B
Emission band spectrum

C
Absorption line spectrum

D
Absorption band spectrum

Solution

When atoms are excited they emit light of certain wavelengths which correspond to different colors and the emitted light is observed as a series of colored lines with dark spaces in between. The series of colored lines are called a line or atomic spectra. Each element produces a unique set of spectral lines and since no two elements emit the same spectral lines, elements can be identified by their line spectrum. It can have either absorption or emission line spectrum depending whether the atom is light or another colliding electron.
Question 5
1 / -0

According to Rutherford atom model, the spectrum emitted by an atom is :

A
Line spectrum

B
Continuous spectrum

C
Continuous absorption spectrum

D
Band spectrum

Solution

One of the defects of Ruherford atom model was if the electrons emit energy continuously, continuous spectrum should be formed. But in practical line spectrum is observed.
Question 6
1 / -0

The ratio of the radii of the first three Bohr Orbits is

A
$$1:\displaystyle \frac{1}{2}:\frac{1}{3}$$

B
$$1:2:3$$

C
$$1:4:9$$

D
$$1:8:27$$

Solution

Radius of $$n^{th}$$ Bohr orbit, $$r_n = 0.529 \dfrac{n^2}{Z}$$ $$A^o$$
$$\implies$$ $$r_n \propto n^2$$
Thus ratio of first three Bohr orbit is $$r_1 : r_2 : r_ 3 = 1^2 : 2^2 : 3^ 2$$
$$\implies$$ $$r_1 : r_2 : r_ 3 = 1 : 4 : 9$$
Question 7
1 / -0

In Hydrogen atom, which of the following transitions produces a spectral line of maximum frequency.

A
$$2\rightarrow 1$$

B
$$6\rightarrow 2$$

C
$$4\rightarrow 3$$

D
$$5\rightarrow 2$$

Solution

The Rydberg formula for Hydrogen atom, $$\dfrac{1}{\lambda}=R[1/n_1^2-1/n_2^2]$$ where $$R=$$ Rydberg constant and $$n_1<n_2$$
For $$2\rightarrow 1$$, $$\dfrac{1}{\lambda_{21}}=R[1/1^2-1/2^2]=(3/4)R=0.75 R$$;
For $$6\rightarrow 2$$, $$\dfrac{1}{\lambda_{62}}=R[1/2^2-1/6^2]=(2/9)R=0.22 R$$;
For $$4\rightarrow 3$$, $$\dfrac{1}{\lambda_{43}}=R[1/3^2-1/4^2]=0.05R$$ and
For $$5\rightarrow 2$$, $$\dfrac{1}{\lambda_{52}}=R[1/2^2-1/5^2]=0.21R$$
Since frequency is inversely proportional to wavelength so $$2\rightarrow 1$$ transition will give the maximum frequency.
Question 8
1 / -0

The number of de Broglie waves of an electron in the $${ n }^{ th }$$ orbit of an atom is :

A
$$n$$

B
$$n-1$$

C
$$n+1$$

D
$$2n$$

Solution

The only places an electron can take in an atom are those where it can complete a multiple of a full wavelength. So when an electron (in wave form) starts from a certain point it must come back to the same point and be at the exact same position as when it started from that point. Otherwise, the wave wouldn't coincide with itself, and it would consequently interfere with itself and possibly destroy itself. This can't happen according to the laws of the conservation of matter and energy, so the electron only takes the orbits in which it can complete a number of full wavelengths. The number of waves is thus $$n$$.
Question 9
1 / -0

In a photon-electron collision ___________.

A
Only total energy is conserved

B
Only total momentum is conserved

C
Both total energy and total momentum are conserved

D
Both total momentum and total energy are not conserved

Solution

In a photon-electron collision both total energy and total momentum are conserved. As in the case of compton effect, when a photon with some energy collides with a stationary electron, some of the energy and momentum is transferred to the electron but both energy and momentum are conserved in this elastic collision.
Option C
Question 10
1 / -0

As the electron in Bohr's orbit of hydrogen atom passes from state $$n=2$$ to, $$n=1$$, the kinetic energy$$(K)$$ and the potential energy $$(U)$$ changes as

A
K four fold, U also four fold

B
K two fold, V also two fold

C
K four fold, U two fold

D
K two fold, U four fold

Solution

Given,
Electron in Bohr's orbit of hydrogen atom passes from state $$n=2$$ to $$n=1$$,
KE of an electron in nth orbit : $$K_n \propto \dfrac{1}{n^2}$$ and PE of an electron in nth orbit : $$U_n\propto \dfrac{1}{n^2}$$
$$\therefore$$ When an electron passes from state n = 2 to n = 1
$$\dfrac{K_2}{K_1}=\dfrac{1^2}{2^2}=\dfrac{1}{4}$$
or $$K_1=4K_2$$
$$\dfrac{U_2}{U_1}=\dfrac{1^2}{2^2}=\dfrac{1}{4}$$
or $$U_1=4U_2$$

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Atoms Test - 42

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Atoms Test - 42

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Question 1

$$1.3\times { 10 }^{ -15 }m$$

$$2.6\times { 10 }^{ -15 }m$$

$$1.3\times { 10 }^{ -13 }m$$

$$2.6\times { 10 }^{ -13 }m$$

Solution

Question 2

Pure line spectrum

Emission band spectrum

Absorption line spectrum

Absorption band spectrum

Solution

Question 3

A stream of electrons

A stream of positive ions

A stream of uncharged particles

The same as canal rays

Solution

Question 4

Pure line spectrum

Emission band spectrum

Absorption line spectrum

Absorption band spectrum

Solution

Question 5

Line spectrum

Continuous spectrum

Continuous absorption spectrum

Band spectrum

Solution

Question 6

$$1:\displaystyle \frac{1}{2}:\frac{1}{3}$$

$$1:2:3$$

$$1:4:9$$

$$1:8:27$$

Solution

Question 7

$$2\rightarrow 1$$

$$6\rightarrow 2$$

$$4\rightarrow 3$$

$$5\rightarrow 2$$

Solution

Question 8

$$n$$

$$n-1$$

$$n+1$$

$$2n$$

Solution

Question 9

Only total energy is conserved

Only total momentum is conserved

Both total energy and total momentum are conserved

Both total momentum and total energy are not conserved

Solution

Question 10

K four fold, U also four fold

K two fold, V also two fold

K four fold, U two fold

K two fold, U four fold

Solution

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