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Which of the following is/are correctly matched?
A.$1atm > 1torr > 1pascal$Units of pressure
B.$SO_4^{2 - } > {N_2} > {O^{2 - }}$Number of electrons per species
C.$1{m^3} > 1L > 1c{m^3}$Units of volume
D.$e > p > \alpha $Specific charge


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Last updated date: 25th Jul 2024
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Answer
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Hint: In order to determine the correct descending order according to the property given, we have to convert them into a common unit and then substitute the value in the given order. For example in the example of unit of pressure we have to convert the all units in one common unit that is $torr$

Complete step by step answer:.
We will be going through each option one at a time and will eliminate the options whose relationship as given in the question is not correct.
Option1: $1atm > 1torr > 1pascal$ (Units of pressure)
In the question we have 3 different units of measurement given to us. To be able to compare between them, we need to convert these values into one unit which is common for all three.
We can convert any two of the units, into the third unit.
So, Let us convert $1atm$ and $1pascal$ into $torr$ .
The conversion factor is:
$1atm = 760torr,1pascal = 0.00750torr$
Hence, the question can be modified as
$760torr > 1torr > 0.00750torr$
This is the correct option.
Option2: $SO_4^{2 - } > {N_2} > {O^{2 - }}$ (Number of electrons per species)
Number of electron in $SO_4^{2 - }$ = ${e^ - }{\text{ of S + 4(}}{{\text{e}}^ - }{\text{ of O) + 2}}$
we know that; $S = 16{e^ - },O = 8{e^ - }$
$ \Rightarrow (16 + 4 \times 8 + 2){e^ - } = 50{e^ - }$
Number of electrons in ${N_2} = {e^ - }{\text{ of N }} \times {\text{ 2}}$
we know that; $N = 7{e^ - }$
$ \Rightarrow (7 \times 2){e^ - } = 14{e^ - }$
Number of electrons in ${O^{2 - }} = {e^ - }{\text{ of O + 2}}$
we know that; $O = 8{e^ - }$
$ \Rightarrow (8 + 2){e^ - } = 10{e^ - }$
Hence, Substituting in the question we get:
$50{e^ - } > 14{e^ - } > 10{e^ - }$
This is correct.
Option3: $1m{l^3} > 1L > 1c{m^3}$ (Units of volume)
Let us convert all the value in centimetres.
The conversion factor is,
$1L = 1000c{m^3},1{m^3} = {10^6}c{m^3}$
Hence, substituting these values in the question we get,
${10^6}c{m^3} > 1000c{m^3} > 1c{m^3}$
this is correct.
Option 4: $e > p > \alpha $ (Specific charge)
Specific charge on $e = 1.7 \times {10^{11}}Ck{g^{ - 1}}$
Specific charge on $p = 9.6 \times {10^7}Ck{g^{ - 1}}$
Specific charge on $\alpha = 4.8 \times {10^7}Ck{g^{ - 1}}$
Substituting these values in the question, we get
$1.7 \times {10^{11}} > 9.6 \times {10^7} > 4.8 \times {10^7}$
This is correct.

So, the correct answer is Option A,B,C,D.

Note: 1. Conversion of these terms should be done to a common unit and one unit should be kept constant. You cannot compare the values unless their units are the same.
2. And also, In calculating the specific charge of the Alpha Particle, you can divide the specific charge of the proton in half and that will be the value of the specific charge on the alpha particle.