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11.(JEE Main 2024 (Online) 30th January Evening Shift )

For the photoelectric effect, the maximum kinetic energy ( E k ) of the photoelectrons is plotted against the frequency ( v ) of the incident photons as shown in figure. The slope of the graph gives

JEE Main 2024 (Online) 30th January Evening Shift Physics - Dual Nature of Radiation Question 15 English

A.Planck's constant

B.Work function of the metal

C.Charge of electron

D.Ratio of planck's constant to electric charge

Correct option is (A)

 K.E.  = hf ϕ tan θ = h

12.(JEE Main 2024 (Online) 30th January Morning Shift )

The work function of a substance is 3.0   eV . The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately;

A.215 nm

B.400 nm

C.414 nm

D.200 nm

Correct option is (C)

 For P.E.E. :  λ h c W e λ 1240   nm eV 3 eV λ 413.33   nm λ max 414   nm  for P.E.E. 

13.(JEE Main 2024 (Online) 27th January Evening Shift )

The threshold frequency of a metal with work function 6.63   eV is :

A. 16 × 10 15   Hz

B. 16 × 10 12   Hz

C. 1.6 × 10 15   Hz

D. 1.6 × 10 15   Hz

Correct option is (C)

1.6 × 10 15   Hz

14.(JEE Main 2024 (Online) 6th April Evening Shift )

In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2   V . The wavelength of light emitted by hydrogen atom when excited to the first excitation level is ________ nm. (Given hc = 1245   eV   nm , e = 1.6 × 10 19 C ).

Correct answer is 122

The Franck-Hertz experiment provides evidence for quantized energy levels within atoms. When atoms are excited by electrons with a specific kinetic energy, they can jump to higher energy levels. Upon returning to lower levels, they emit photons whose energies correspond to the difference between these levels. The first dip in the current-voltage graph for hydrogen, observed at 10.2 V, corresponds to the energy required to excite a hydrogen atom to its first excitation level. The wavelength of the light emitted when the atom returns to its ground state can be calculated using the energy of the photon emitted.

To find the wavelength (λ) of light emitted, we use the relationship between energy (E), Planck's constant (h), the speed of light (c), and wavelength (λ), given in the equation form as E=hcλ.

However, we are given hc in electron volts per nanometer (1245 eVnm), and the energy is also given in terms of voltage (10.2 V). First, we convert the energy into electron volts (eV) using the formula: E=eV, where e is the charge of an electron (1.6×1019C).

The energy in electron volts can be directly calculated as:

E=10.2 V1.6×1019C/electron=10.2 eV,

since 1 V1 C=1 eV by definition.

Next, using the energy-wavelength relationship and the given value for hc, the wavelength can be calculated as:

λ=hcE

Substituting the given values yields:

λ=1245 eVnm10.2 eV

This simplifies to:

λ=124510.2 nm

Calculating this gives:

λ122.06 nm.

Therefore, the wavelength of light emitted by the hydrogen atom when excited to the first excitation level is approximately 122.06 nm.