Dual Nature Of Radiation And Matter

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The graph $\frac{1}{λ}$ and stopping potential (V) of three metals having work function $ϕ_{1}, ϕ_{2} and ϕ_{3}$ in an experiment of photoelectric effect is plotted as shown in the figure. Which one of the following statement is/are correct? [Here λ is the wavelength of the incident ray ]

(i) Ratio of work functions $ϕ_{1} : ϕ_{2} : ϕ_{3}$ = 1 : 2 : 4
(ii) Ratio of work functions $ϕ_{1} : ϕ_{2} : ϕ_{3}$ = 4 : 2 : 1
(iii) tanθ ∝ $\frac{h c}{e}$ , where h = Planck's constant, c = speed of light
(iv)The violet colour-light can eject photoelectrons from metals 2 and 3

(i), (iii)

(i), (iv)

(ii), (iii)

(i), (ii) and (iv)

Solution

(i), (iii)

According to Einstein photoelectric equation,

E = K_max + $ϕ$

$\frac{h c}{λ}$ = $ϕ$ + eV_s

∴ V_s = $[\frac{hc}{λ} - ϕ]$ $\frac{1}{e}$

V_s versus $\frac{1}{λ}$ graph is a straight line.

Slope

$tanθ = \frac{h c}{e}$

The curves intersect the $\frac{1}{λ}$ axis, where V_s is zero

∴ $\frac{h c}{λ} - ϕ$ = 0

⇒ $\frac{1}{λ}$ = $\frac{ϕ}{h c}$

For metal 1

$\frac{ϕ_{1}}{h c} = 0.001$

For metal 2

$\frac{ϕ_{2}}{hc}$ = 0.002

For metal 3

$\frac{ϕ_{3}}{hc}$ = 0.004

∴ $ϕ_{1} : ϕ_{2} : ϕ_{3}$ = 1 : 2 : 4

For metal 1

$λ_{O_{1}} = \frac{hc}{ϕ} = \frac{1}{0.001}$ = 1000 nm

For metal 2, threshold wavelength,

$λ_{O_{2}} = \frac{hc}{ϕ}$ = $\frac{1}{0.002}$ = 500 nm

Simillarly,

$λ_{O_{3}} = \frac{hc}{ϕ} = \frac{1}{0.004}$ = 250 nm

λ_voilet = 400 nm

For metal 1

λ_voilet < λ_threshold

For metal 3

λ_voilet > λ_threshold

Some More Questions From Dual Nature of Radiation and Matter Chapter

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Dual Nature Of Radiation And Matter

Some More Questions From Dual Nature of Radiation and Matter Chapter

The time by a photoelectron to come out after the photon strikes is approximately

An alpha nucleus of energy 1 /2 mv² bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to

If I₀ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

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For Daily Free Study Material Join wiredfaculty

Dual Nature Of Radiation And Matter

Some More Questions From Dual Nature of Radiation and Matter Chapter

The time by a photoelectron to come out after the photon strikes is approximately

An alpha nucleus of energy 1 /2 mv2 bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to

If I0 is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young’s double-slit experiment is

According to Einstein’s photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal Vs the frequency, of the incident radiation gives straight line whose slope

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

An alpha nucleus of energy 1 /2 mv² bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to

If I₀ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?