Chemistry

What is the wavelength of the light emitted when the electron in a hydrogen atom undergoes transition from the energy level with n = 4 to energy level n = 2? What is the colour corresponding to this wavelength? (Given R_H = 109678 cm^-1)

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According to Balmer formula,

Wave number (? ) = R_H [1/n₁²- 1/n₂²]cm^-1

= 109678 [1/2² – 1/4²] cm^-1

= (109678 x 3) / 16 cm^-1

λ = 1 /? = 16 / (109678 x 3) cm = 16 x 10⁷ / (109678 x 3) nm = 486 nm

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9 months ago

Electrons are emitted with zero velocity from a metal surface when it is exposed to radiation of wavelength 6800 Å. Calculate threshold frequency (v₀) and work function (W₀) of the metal.

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Threshold frequency (v₀) = c /λ = (3 * 10⁸ m s^-1) / (68 x 10^-8 m) = 4.41 x 10¹⁴ s^-1

Work function (W₀) = hv₀= (6.626 * 10^-34 Js) x (4.41 x 10¹⁴ s^-1) = 2.92 x 10^-19 J.

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9 months ago

A 25 watt bulb emits monochromatic yellow light of wavelength 0.57 μm. Calculate the rate of emission of quanta per second.

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Energy of one photon (E) = hc / λ

= (6.626 * 10^-34 Js) x (3 * 10⁸ m s^-1) / (0.57 * 10^-6 m) = 3.48 x 10^-19J

Rate of emission of quanta per second = Power / Energy = (25 watt) / (3.48 x 10^-19 J)

= (25 Js^-1) / (3.48 x 10^-19 J) = 7.18 x 10¹⁹ s^-1

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9 months ago

Electromagnetic radiation of wavelength 242 nm is just sufficient to ionise the sodium atom. Calculate the ionisation energy of sodium in kJ mol^-1.

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Given: λ = 242 nm = 142 x 10^-9 m, c = 3 x 10⁸ ms^-1, h = 6.626 x 10^-34Js

We know, E = hc / λ

= (6.626 * 10^-34 Js) x (3 * 10⁸ m s^-1) / (242 * 10^-9 m) = 0.0821 x 10^-17 J

∴ Ionization energy per mol (E) = (0.0821 x 10^-17 J) x (6.022 x 10²³ mol^-1J) / 1000 = 494 kJ mol^-1

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9 months ago

A photon of wavelength 4 * 10^-7 m strikes on metal surface; the work function of the metal being 2.13 eV. Calculate

(i) The energy of the photon,

(ii) The kinetic energy of the emission

(iii) The velocity of the photoelectron. (Given 1 eV = 1.6020 * 10^-19 J).

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Contributor-Level 10

(i) Energy of photon (E) = hc / λ

= (6.626 * 10^-34 Js) x (3 * 10⁸ m s^-1) / (4 * 10^-7 m) = 4.969 x 10^-19 J

Since, 1.6020 * 10^-19 J= 1 eV

So, 1 J= (1 eV) / (1.6020 * 10^-19 J)

Hence, 4.969 x 10^-19 J = (1eV) x (4.969 x 10^-19 J) / (1.602 x 10^-19J) = 3.1 eV

(ii) Kinetic energy of emission = Energy – work function

= (3.1 – 2.13) = 0.97 eV

(iii) Kinetic energy of emission = 0.97 eV

=> ½ mv²= 0.97 eV = 0.97 x 1.602 x 10^-19 J = 0.97 x 1.602 x 10^-19kg m² s^-2

=> v²= (2 x 0.97 x 1.602 x 10^-19kg m² s^-2) / (9.1 x 10^-31 kg) = 0.34 x 10¹² m² s^-2

=> v = (0.34 x 10¹² m² s^-2)^1/2= 0.583 x 10⁶ ms^-1 = 5.83 x 10⁵ ms^-1

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9 months ago

What is the number of photons of light with wavelength 4000 pm which provide 1 Joule of energy?

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Contributor-Level 10

Given: h = 6.626 * 10^-34 Js,

c = 3 * 10⁸ m s^-1,

λ = 4000 pm = 4000 * 10^-12 m = 4 * 10^-9 m

Energy of photon (E) = hc / λ

= (6.626 * 10^-34 Js) x (3 * 10⁸ m s^-1) / (4 * 10^-9 m) = 4.969 x 10^-17 J

i.e. 4.969 x 10^-17 J is the energy of 1 photon

Therefore, 1 J is the energy of photons = 1 / (4.969 x 10^-17) = 2.012 x 10¹⁶ photons.

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9 months ago

Calculate the wavelength, frequency, and wavenumber of lightwave whose period is 2.0 * 10^-10 s.

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Wavelength, λ = (3 * 10⁸ ms^-1) / (5 * 10⁹s^-1) = 6.0 x 10^-2 m

Frequency, ν = 1 / 2.0 * 10^-10 s = 5.0 x 10⁹ s^-1

Wavenumber, (? ) = 1 / (6.0 x 10^-2 m) = 16.66 m^-1

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9 months ago

Calculate the energy of each of the photons which

(i) Correspond to light of frequency 3 * 10¹⁵ Hz

(ii) Have wavelength of 0.50 Å.

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Contributor-Level 10

(i) Energy of photon (E) = hν, where h= Plank's const, ν= Frequency

h= 6.626 * 10^-34 J s ; ν = 3 * 10¹⁵ Hz = 3 * 10¹⁵s^-1

∴ E = (6.626 * 10^-34 J s) * (3 * 10¹⁵ s^-1) = 1.986 * 10¹⁸ J

(ii) Energy of photon (E) = hν = hc/λ, where λ= wavelength

h = 6.626 * 10^-34 J s ; c = 3 * 10⁸ m s^-1 λ= 0.50 Å = 0.5 * 10^-10 m.

∴ E = (6.626 * 10^-34 J s) * (3 * 10⁸ ms^-1) / 0.5 * 10^-10 m = 3.98 x 10^-15 J.

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9 months ago

Write the complete symbol for the atom (X) with the given atomic number (Z) and atomic mass (A)

(i) Z = 17,A = 35

(ii) Z = 92, A = 233

(iii) Z = 4, A = 9

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Kindly go through the solution.

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