What is the wavelength of the photons emitted by hydrogen atoms when they undergo transitions fr

What is the wavelength of the photons emitted by hydrogen...

Key Concepts

Hydrogen Emission Spectrum

The hydrogen emission spectrum is a series of characteristic lines produced when electrons in a hydrogen atom transition between energy levels. Each series, such as the Lyman, Balmer, or Paschen series, corresponds to transitions that end at a specific energy level, reflecting the quantized nature of atomic energy states.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all forms of electromagnetic radiation, organized by wavelength or frequency. Identifying the region of the electromagnetic spectrum where a particular spectral line falls helps in understanding the energy and potential applications of the radiation. In the context of atomic transitions, this involves determining whether the emitted light is ultraviolet, visible, infrared, etc.

Rydberg Equation

The Rydberg equation is used to determine the wavelengths of photons emitted or absorbed by hydrogen-like atoms as electrons transition between energy levels. It relates the reciprocal of the wavelength to the difference between the inverses of the squares of the principal quantum numbers, thereby providing a mathematical description of spectral lines.

Energy Level Transitions

This concept refers to the movement of an electron between distinct energy levels in an atom. When an electron moves from a higher to a lower energy level, it emits a photon whose energy equals the difference between the two levels. Understanding energy level transitions is crucial for explaining atomic emission or absorption spectra.

Transcript

00:03 Hello.

00:05 So the question that is asked here is related to the bohr model of an atom.

00:10 So the question is what is the wavelength of photons emitted by hydrogen atom when they undergo transition from n is equal to 4 to n is equal to 3? n is the principal quantum number and in which reason of the electromagnetic spectrum does these radiation occur? so it is like transition form if we take these as states.

00:34 So and 1 n is equal to 1, n is equal to 2, n is equal to 3, n is equal to 4.

00:43 When transition from 4 to 3 takes place, the energy emission corresponding to that can be written as e is equal to minus 13 .6 in terms of electron volt, one over final state quantum number, that is n, let us say, n f square minus 1 over an initial square.

01:08 Okay, in turn, unity is electron volts.

01:12 So that will be equal to minus 13 .6 into 1 over nf is 3 square minus 1 by 4 square.

01:23 So from here the value of energy will be minus 13 .6 into 16 minus 9 is 7 over 16 into 9 electron volt.

01:38 So we know that 11 electron volt is equal to 1 .6 into 10 to the power minus 19 in june.

01:47 Now we need to evaluate the value of wavelength.

01:50 And to evaluate the value of wavelength, let us convert this electron volts into jule.

01:57 So from here, we get the energy value is equal to minus 13 .6 into 7 over 16 into 9 into 1 .6 into 10 to the power minus 19 jule.

02:11 Okay.

02:12 This is the required value of energy.

02:14 Now take the mode of this energy.

02:16 I mean take this value positive because wavelength can never be negative.

02:20 So energy we know that can be written as hc by lambda.

02:24 That is equal to 13 .6.

02:26 This will be cancelled...

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