Dual Nature of Radiation and Matter Test

Result

Dual Nature of Radiation and Matter Test - 71

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Weekly Quiz Competition

Question 1
1 / -0

What is the wavelength $$(\mathring{ A } )$$ of a photon that has an energy of $$4.38 \times 10^{-18}$$ J?

A
$$454\ \mathring{ A } $$

B
$$2.3 \times 10^7\ \mathring{ A } $$

C
$$6.89 \times 10^{15}\ \mathring{ A } $$

D
$$1.45 \times 10^{-15}\ \mathring{ A } $$

Solution
Question 2
1 / -0

A subatomic particle of mass $$10^{-18} \mu g$$ is in thermal equilibrium with its surrounding at temperature of 400 K. Then the wave length of this particle will be

A
$$48.2 A^o$$

B
$$2.8 A^o$$

C
$$12.7 A^o$$

D
$$142 A^o$$
Question 3
1 / -0

An element undergoes a reaction as shown: $$X+2e^− \to X^{ 2−}$$
Energy released = 30.87 eV/ atom. If the energy released, is used to dissociate 4 g of $$H_2$$ molecules, equally into $$H^{+}$$ and$$H^{*}$$, where $$H^{*}$$ is excited state of H atoms where the electron travels in orbit whose circumference equal to four times its de Broglie's wavelength. Determine the least moles of X that would be required :
Given : I.E of H = 13.6 eV/atom, bond energy of $$H_2$$ = 4.526 eV /molecule.

A
1

B
2

C
3

D
4

Solution
Question 4
1 / -0

The frequency of line spectrum of sodium is $$5.09\times 10^{14} sec^{-1}$$. Its wavelength ( in nm) will be -[ $$C=3\times 10^8 $$m/sec]

A
$$510 $$ nm

B
$$420 $$ nm

C
$$589 $$ nm

D
$$622 $$ nm

Solution
Question 5
1 / -0

The accelerating potential that must be imparted to a proton beam to given it an effective wavelength of 0.05 nm is
(At. of proton = 1.008 g)

A
0.325 V

B
5.205 V

C
52.05 V

D
3.25 V

Solution

Wavelength of proton, $$\lambda = 0.05\times10^{-9}m$$
Mass of proton $$m = 1.67\times 10^{-27}kg$$
Charge on proton, $$q = 1.6\times 10^{-19}C$$

Using, $$p = mv=\dfrac {h}{\lambda}$$

$$v = \dfrac{6.6\times 10^{-34}}{1.67\times10^{-27}\times0.05\times 10^{-9}} = 7.904 \times 10^3m/s$$

Now potential energy due to accelerating potential will provide kinetic energy to proton,

$$qV = \dfrac12mv^2$$

$$V = \dfrac{1.67\times 10^{-27}\times (7.904\times 10^3)^2}{2\times 1.6\times 10^{-19}}$$

$$V =0.326$$ $$V$$
Question 6
1 / -0

A metal have work function 4 eV is exposed to photon of $$\lambda =1240\AA .$$ If a accelerating potential of 7.6 volt is applied, then the electron with maximum kinetic energy will have speed equal to

A
$$2.18\times 10^{6}m/s$$

B
$$3\times 10^{8}m/s$$

C
$$9.61\times 10^{5}m/s$$

D
$$8.72\times 10^{6}m/s$$

Solution
Question 7
1 / -0

If $$E_e, E_a$$, and $$E_p$$ represents the kinetic energies of an electron alpha particle and a proton respectively, each moving with same De-Broglie wavelength then :

A
$$E_e = E_{\alpha} = E_p$$

B
$$E_e > E_{\alpha} > E_p$$

C
$$E_{\alpha} < E_p < E_e$$

D
$$E_e = E_p < E_n$$

Solution
Question 8
1 / -0

When the light of frequency 2$${ v }_{ 0 }$$(where $${ v }_{ 0 }$$ is the threshold frequency), is incident on a metal plate the maximum velocity of electrons emitted is $${ v }_{ 1 }$$ .When the frequency of the incident radiation is increased to 5$${ v }_{ 0 }$$.The maximum velocity of electrons emitted from the same plate is $${ v }_{ 2 }$$.The ratio of $${ v }_{ 1 } to { v }_{ 2 }$$ is

A
1:2

B
1:4

C
2:1

D
4:1

Solution

Using Einstein's photoelectric equation$$,$$
$$E = {W_0} + {K_{\max }}$$
when light of frequency$$,2{v_0}$$ is incident on a meal plate$$,$$
$$h\left( {2{v_0}} \right) = h{v_0} + \dfrac{1}{2}m{v_1}^2$$
$$h{v_0} = \dfrac{1}{2}m{v_1}^2$$---------------$$(1)$$
when light of frequency$$,5{v_0}$$ is incident on a metal plate
$$h\left( {5{v_0}} \right) = h{v_0} + \dfrac{1}{2}m{v_2}^2$$
$$h{v_0} = \dfrac{1}{2}m{v_2}^2$$----------------$$(2)$$
Dividing equation $$(1)$$ and $$(2)$$
$$\dfrac{1}{4} = \dfrac{{\dfrac{{\sqrt 2 }}{1}}}{{\dfrac{{\sqrt 2 }}{2}}}$$
$$\therefore \dfrac{{{v_1}}}{{{v_2}}} = \dfrac{1}{2}$$
Hence,
option $$(A)$$ is correct answer.
Question 9
1 / -0

When electron are de-exciting from nth orbit of hydrogen atoms, 15 spectral lines are formed. The shortest wavelength among these wil be

A
$$\cfrac {11} {900}R$$

B
$$\cfrac {900} {11}R$$

C
$$\cfrac {35} {36}R$$

D
$$\cfrac {36} {35}R$$

Solution
Question 10
1 / -0

A photon of wavelength $$6200A^{o}$$ was incident on a metal whose threshold frequency was $$12400A^{o}$$ cal the $$kE$$ with which electron was emited?

A
$$1.6\times 10^{23}\ J$$

B
$$3.16\times 10^{-19}\ J$$

C
$$1.6\times 10^{+19}\ J$$

D
$$6.02\times 10^{+23}\ J$$

Solution