Dual Nature of Radiation and Matter — Page 10 | NEET Physics

Q91

The de Broglie wavelengths for an electron and a photon are

\lambda

e and

\lambda

p respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two ?

A

{\lambda _p} \propto \lambda _e^2

B

{\lambda _p} \propto {\lambda _e}

C

{\lambda _p} \propto \sqrt {{\lambda _e}}

D

{\lambda _p} \propto \sqrt {{1 \over {{\lambda _e}}}}

Correct Answer

Option A

Solution

{\lambda _p} = {h \over p} = {{hc} \over E}

...... (i)

{\lambda _e} = {h \over {\sqrt {2mE} }}

...... (ii) From (i) and (ii)

{\lambda _p} \propto \lambda _e^2

Q92

A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass ' 4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths

{{{\lambda _A}} \over {{\lambda _B}}}

is close to :

A 4.47

B 10.00

C 14.14

D 0.07

Correct Answer

Option C

Solution

K.E. acquired by charge = K = qV $\lambda$ =

{h \over P}

=

{h \over {\sqrt {2mK} }}

=

{h \over {\sqrt {2mqV} }}

$\therefore$

{{{\lambda _A}} \over {{\lambda _B}}} = {{\sqrt {2m{}_B{q_B}{V_B}} } \over {\sqrt {2m{}_A{q_A}{V_A}} }} = \sqrt {{{4m.q.2500} \over {m.q.50}}} = 2\sqrt {50}

= 2 \times 7.07 = 14.14

Q93

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10–12 m, the minimum electron energy required is close to -

A 25 keV

B 500 keV

C 100 keV

D 1 keV

Correct Answer

Option A

Solution

$\lambda$ =

{h \over p}

{ $\lambda$ = 7.5 $\times$ 10 $-$ 12} P =

{h \over \lambda }

KE =

{{{P^2}} \over {2m}} = {{{{\left( {h/\lambda } \right)}^2}} \over {2m}}

= {{\left\{ {{{6.6 \times {{10}^{ - 34}}} \over {7.5 \times {{10}^{ - 12}}}}} \right\}} \over {2 \times 9.1 \times {{10}^{ - 31}}}}

J KE = 25 Kev

Q94

The threshold wavelength for photoelectric emission from a material is 5500

\mathop A\limits^o

. Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a A. 75 W infra-red lamp B. 10 W infra-red lamp C. 75 W ultra-violet lamp D. 10 W ultra-violet lamp Choose the correct answer from the options given below :

A C only

B A and D only

C C and D only

D B and C only

Correct Answer

Option C

Solution

Wavelength of infra-red $=700 \mathrm{~nm}$ (minimum) Wavelength of UV $=100-400 \mathrm{~nm}$ Since we need $\lambda<5000$ Å $\Rightarrow$ Only UV would be able to emit photoelectrons.

Q95

Formation of covalent bonds in compounds exhibits

A wave nature of electron

B particle nature of electron

C both wave and particle nature of electron

D none of these

Correct Answer

Option A

Solution

Formation of covalent bond is best explained by molecular orbital theory.

Q96

In a photoelectric effect experiment a light of frequency 1.5 times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electrons emitted will be:

A doubled

B halved

C Zero

D quadrupled

Correct Answer

Option C

Solution

Since

\frac{\mathrm{f}}{2} i.e. the incident frequency is less than threshold frequency. Hence there will be no emission of photoelectrons.

\Rightarrow \text { current }=0$$