Atoms Test

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Atoms Test - 36

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Weekly Quiz Competition

Question 1
1 / -0

If in hydrogen atom, radius of $$n^{th}$$ Bohr orbits is $$r_n$$, frequency of revolution of electron in $$n^{th}$$ orbit is $$f_n$$, choose the correct option.

A

B

C

D
Both (a) and (b)

Solution

Radius of $$n^{th}$$ orbit $$r_n \infty n^2$$, graph between $$r_n$$ and $$n$$ is a parabola. Also, $$\displaystyle \frac{r_n}{r_1} = \left(\frac{n}{1}\right)^2 \Rightarrow log_e\left(\frac{r_n}{r_1}\right) = 2log_e(n)$$
Comparing this equation with $$y = mx + c$$,
Graph between $$\displaystyle log_e \left(\frac{r_n}{r_1}\right)$$ and $$log_e(n)$$ will be straight line, passing from origin.
Similarly it can be proved that graph between $$\displaystyle log_e \left(\frac{f_n}{f_1} \right)$$ and $$log_e(n)$$ is a straight line. But with negative slops.
Question 2
1 / -0

The specific charge for cathode rays is

A
Constant

B
Variable

C
Depend upon the material of the cathode

D
Depend upon the nature of the gas in the discharge tube

Solution

Cathode rays (also called an electron beam or e-beam) are streams of electrons observed in vacuum tubes.
Charge $$=-e$$
Mass $$=m_e$$
Specific Charge $$=\cfrac{Charge}{Mass} = \cfrac{e}{m_e}$$= Constant
Question 3
1 / -0

A photon will have less energy, if its

A
Amplitude is higher

B
Frequency is higher

C
Wavelength is longer

D
Wavelength is shorter

Solution

Energy of photon = $$\dfrac{hc}{\lambda}$$
Hence, a photon with longer wavelenght will carry less energy.
Question 4
1 / -0

Photons have the following characteristics:
(i) energy of a photon $$E=h\gamma$$
(ii) photons travel with the velocity of light
(iii) photons are emitted when light of frequency $$\gamma$$ is emitted by an atom

A
(i), (ii)

B
(ii), (iii)

C
(i), (ii) and (iii)

D
Only (i)
Solution
(i), (ii), (iii)
A photon is a particle of light defined as discrete bundles or quantum of electromagnetic energy.
Properties of photon :
Photons always moves with the speed of light.
Photons are electrically neutral
Photons have no mass but they have energy.
$$E= hv$$ where h is the planks constant.
The energy of each photon is inversely proportional to the wavelength of the associated EM wave.
$$E= hv= h\cfrac{c}{\lambda}$$
Photons can be created or destroyed.
Question 5
1 / -0

Directions For Questions

A Rydberg hydrogenic atom is one in which the electron possesses a very large quantum number e.g. $$ n = 100 $$ . Take the electron charge to be $$ -e (e > 0) $$ . The binding energy of the Rydberg electron may be taken as $$ E_b = 10_{3} eV $$.

...view full instructions

Let the energy of the electron confined in the atom be $$E$$ . At what $$F_0$$ would the atom ionize?

A
$$\displaystyle F_0 = \frac {E^2 \pi \varepsilon_0} {e} $$

B
$$\displaystyle F_0 = \frac {E^2 \varepsilon_0} {e^3} $$

C
$$\displaystyle F_0 = \frac { \pi \varepsilon_0} {e^3} $$

D
$$\displaystyle F_0 = \frac {E^2 \pi \varepsilon_0} {e^3} $$
Question 6
1 / -0

The Bohr's orbit radius for the hydrogen atom (n = 1) is approximately 0.53 A. The radius for the first excited state (n = 2) orbit is:

A
0.27 A

B
1.27 A

C
2.12 A

D
3.12 A

Solution

Radius of nth orbit of hydrogen atom
$$r_m = 0.529 \times n^2$$
Given n = 2 (where n is no. of orbit)

$$\therefore r_n = 0.529 \times (2)^2 = 2.12 A$$
Question 7
1 / -0

To get line spectrum, the substances are excited in their

A
Solid state

B
Molecular state

C
Gaseous state

D
Atomic state

Solution

A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to identify atoms and molecules from their characteristic spectral lines. The characteristics spectral is produced by exciting them into atomic state.
Question 8
1 / -0

For the same kinetic energy, the momentum shall be maximum for

A
Electron

B
Proton

C
Deutron

D
Alpha particle

Solution

$$ \begin{array}{l} \text { We know that, } \\ \qquad k=\frac{p^{2}}{2 m}\left\{\begin{array}{c} \text { Where, } k=\text { kinetic energy } \\ p \text { =momentum } \\ m=\text { mass } \end{array}\right. \end{array} $$
$$ \begin{array}{l} P=\sqrt{2 m k} \\ P \alpha \sqrt{m}\{K \text { is constant given }\} \end{array} $$
$$ \begin{array}{l} \therefore \alpha \text { - Particle has greater mass.then proton, neutron } \\ \therefore \text { Momentum of } \alpha \text { -particle is more and maximum } \\ \text { (D) Alpha particle is correct } \end{array} $$
Question 9
1 / -0

The radius of a nucleus with mass number 16 is 3 fm. The radius of another nucleus with mass number 128 is

A
6 fm

B
12 fm

C
18 fm

D
24 fm

Solution

We know that the radius of nucleus $$R$$ is related with the mass number $$A$$ by following relation:
$$R\propto A ^{1/3}$$

$$\dfrac{R_{2}}{R_{1}}=(\dfrac{A_{2}}{A_{1}})^{1/3}$$

Given: $$A_{1}=16 , A_{2}=128 , R_{1}=3\ fm , R_{2}=?$$

Hence, $$\dfrac{R_{2}}{3}=(\dfrac{128}{16})^{1/3}$$

  $$\dfrac{R_{2}}{3}=(\dfrac{8}{1})^{1/3}$$

  $$\dfrac{R_{2}}{3}=({2}^{3})^{1/3}$$

  $$\dfrac{R_{2}}{3}=2$$

$$R_{2}=6fm$$
Question 10
1 / -0

The spectrum of light emitted by an electric bulb is an example of

A
Emission spectrum

B
Absorption spectrum

C
Continuous spectrum

D
Line spectrum

Solution

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Atoms Test - 36

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Atoms Test - 36

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Question 1

Both (a) and (b)

Solution

Question 2

Constant

Variable

Depend upon the material of the cathode

Depend upon the nature of the gas in the discharge tube

Solution

Question 3

Amplitude is higher

Frequency is higher

Wavelength is longer

Wavelength is shorter

Solution

Question 4

(i), (ii)

(ii), (iii)

(i), (ii) and (iii)

Only (i)

Solution

Question 5

$$\displaystyle F_0 = \frac {E^2 \pi \varepsilon_0} {e} $$

$$\displaystyle F_0 = \frac {E^2 \varepsilon_0} {e^3} $$

$$\displaystyle F_0 = \frac { \pi \varepsilon_0} {e^3} $$

$$\displaystyle F_0 = \frac {E^2 \pi \varepsilon_0} {e^3} $$

Question 6

0.27 A

1.27 A

2.12 A

3.12 A

Solution

Question 7

Solid state

Molecular state

Gaseous state

Atomic state

Solution

Question 8

Electron

Proton

Deutron

Alpha particle

Solution

Question 9

6 fm

12 fm

18 fm

24 fm

Solution

Question 10

Emission spectrum

Absorption spectrum

Continuous spectrum

Line spectrum

Solution

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