Question

When an electron drops from the m shell (n = 3) to a vacancy in the k shell (n = 1), the measured wavelength of the emitted x-ray is found to be 0.101 nm. Identify the element. Ans: gallium (z=31)?

Answer 1

Explanation:

simplify from next then u will get the answer

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Answer 2

Answer:

Gallium has been recognized as the element.

Explanation:

What is an electron transition?

An atomic electron transition occurs when an electron moves (or jumps) from one energy level to another inside of an atom or synthetic atom. As the electron "jumps" from one quantized energy level to another, usually in a few nanoseconds or less, it appears discontinuous. It is sometimes referred to as an atomic transition, an electronic (de-)excitation, or a quantum jump.

Emission or absorption of electromagnetic radiation in the form of quantized particles known as photons results from electron transitions. The distribution of the time between jumps is exponential, and their statistics are Poissonian. The natural, pressure, and field broadening of spectral lines are related to the damping time constant, which has a range of nanoseconds to a few seconds. The wavelength of the photon released is inversely proportional to the energy gap between the states the electron jumps between.

Calculation:

Given: $n_{1}$= 1, $n_{2}$ = 3

For a given element of an electron transition,

$\frac{1}{ \lambda} = R [\frac{1}{n_{1} ^{2} } -\frac{1}{n_{2} ^{2} } ]$

$\frac{1}{ \lambda} =$  $R[1-\frac{1}{9}]$

$\frac{1}{ \lambda} = \frac{1}{R} [\frac{9}{8} ]$

R = $\lambda[\frac{9}{8}]$

R = $0.101 * 10^{-9} * 1.125$

R = 1136 ${\AA}$

As, we can see from the given value the element will be gallium.

The element which is identified is gallium.

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