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Assertion: K-shell electron capture is detected by analyzing the wavelength of $X-Ray$ emitted.
Reason: The wavelength of the $X-Ray$ is characteristic of the daughter element and not the parent element.
A.Both assertion and Reason are true and Reason is the correct explanation of Assertion.
B.Both Assertion and reason are true but Reason is not the correct explanation of Assertion.
C.Assertion is true but Reason is false.
D.Assertion is false but Reason is true.
E.Both Assertion and Reason are false.

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Last updated date: 22nd Feb 2024
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Hint:In the process of electron capture the proton-rich nucleus of an atom which has zero electrical charge absorbs an inner atomic electron, and converts the proton of that element into a neutron.
-In this process electron neutrino is produced which has the characteristic of the element which is being formed after the process.

Complete step by step answer:
 Electron capture can be defined as a process in which the proton-rich nucleus of an atom which is electrically neutral absorbs an inner atomic electron, usually from electrons of the K or L shells. This process therefore, converts a nuclear proton into a neutron and at the same time causes the emission of an electron neutrino. This process can be generally represented by and equation given below,
\[p+{{e}^{-}}\to n+{{v}_{e}}\]
Here $p$ represents the proton carried by that atom, the symbol ${{e}^{-}}$ represents the electron of that atom, the $n$ represents neutron of that atom and finally the ${{v}_{e}}$ represents the electron neutrino, which is nothing but a subatomic particle which doesn’t have any net electric charge, or in other words its net electric charge is zero.
Now in the given question we can see that the nucleus of one of the atoms traps an electron from the K-shell which converts the proton of that atom to a neutron. It is common in nuclei having $Z>10$ , as it is being mentioned it is the nucleus of an element of the K-shell.
$_{56}B{{a}^{133}}{{+}_{-1}}{{e}^{0}}{{\to }_{55}}C{{s}^{133}}+X-ray$
As we can see the $X-Ray$ emitted by the process can be analyzed in order to detect the k-shell electron capture.
We know that the wavelength of the $X-Ray$ emitted by the process would have the characteristic of the daughter element and not the parent element, which means, the element which is formed after this process as a product is the daughter element and the $X-Ray$ emitted by it, would have the characteristic corresponding to the product.
Hence, Both Assertion and Reason are true but the Reason is not the correct explanation of given Assertion.
So the correct option is option B.

Note:
-When an element captures electrons from the K-shell, it converts the proton of that element to a neutron and in this process $X-Ray$ is being emitted.
-The $X-Ray$ emitted in this process would have the characteristic of the element which is formed after the capture of electrons and conversion of proton into the neutron.
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