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Question: The sodium flame test has a characteristic yellow color due to emission of wavelength \[589nm.\] wha...

The sodium flame test has a characteristic yellow color due to emission of wavelength 589nm.589nm. what is the mass equivalent of one photon of this wavelength?

Explanation

Solution

The amount of energy which is carried by a proton is called the energy of a photon.
In this question we will first find the energy of the photon and then we will equate that energy to mass energy equivalence equation. From mass energy equivalence we can calculate the mass equivalent of a photon as asked in the question.

Complete step by step answer:
To calculate the mass equivalent of one photon we first need to find the photon's energy.
We will calculate photon energy using the following formula
E=h×cλE=\dfrac{h\times c}{\lambda } ………… (i)
Here E=E=energy of photon
h = planck's constant =6.626×10−34Js6.626\times {{10}^{-34}}Js
c = speed of light = 3×108m/s3\times {{10}^{8}}m/s
λ=\lambda = Wavelength of photon = 589nm=598×10−9m589nm=598\times {{10}^{-9}}m
Using these given values and putting them in the (i) formula we will get,
E=6.626×10−34×3×108598×10−9E=\dfrac{6.626\times {{10}^{-34}}\times 3\times {{10}^{8}}}{598\times {{10}^{-9}}} ………. (ii)
On solving (ii) we will get value of energy of photon i.e. E
E=3.37×10−19JE=3.37\times {{10}^{-19}}J
From mass energy equivalence we know,
E=mc2E=m{{c}^{2}} …… (iii)
E = energy :
3.37×10−193.37\times {{10}^{-19}}
M= mass
c2{{c}^{2}}= speed of light :
(3×108)2{{(3\times {{10}^{8}})}^{2}}
Using above data and putting them into (iii) we will get mass equivalent of the photon
3.37×10−19=m×(3×108)23.37\times {{10}^{-19}}=m\times {{(3\times {{10}^{8}})}^{2}}
M=3.37×10−363.37\times {{10}^{-36}}kg
The mass equivalent of photon is 3.37×10−363.37\times {{10}^{-36}} kg because valency of sodium is 1

Additional Information:
The main motive of Flame test is to notice the characteristic colour which are formed by certain metallic ions on being vaporized in a flame and then to recognize an unknown metallic ion by using flame test.
In the presence of concentrated HCL (in flame test) some metal compounds form colored flames. In flame test metal compounds become volatile and the vapors form different colored flames. Concentrated HCL changes metal into their respective metallic chlorides and these chlorides are volatile.

Note: Mass equivalent is defined as the mass of a substance in grams that integrates with or is chemically equal to 11 gm hydrogen or 88 gm oxygen or it is weight of substance divided by valence electron.