The Question is from neet-physics units-and-measurement , and it was created by the author P.NARASIMHA

Question

The ionization energy of hydrogen is 13.6 eV. Express this energy in joules per mole using the following conversions: 1 eV = $1.602 	imes 10^{-19}$ J and Avogadro's number = $6.022 	imes 10^{23}$  $mol^{-1}$.

P.NARASIMHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: Option C
## CONCEPT FRAMEWORK
	**Primary Concept**: Conversion of units and calculating energy per mole.
	**Related Topics**: Ionization energy, unit conversion, Avogadro's number.
	**Prerequisites**: Understanding of ionization energy, conversion factors, and Avogadro's number.
## SOLUTION PATHWAY
**Given Information**:
	Ionization energy of hydrogen = 13.6 eV
	1 eV = $1.602 	imes 10^{-19}$ J
	Avogadro's number = $6.022 	imes 10^{23}$ $mol^{-1}$
**Method & Steps**:
	1. Convert ionization energy from eV to Joules.
		Reasoning: To express the energy in joules, we need to use the given conversion factor.
		Formula/Rule: $Energy (J) = Energy (eV) 	imes Conversion Factor (J/eV)$
	2. Calculate energy per mole.
		Working: Convert the energy from joules per atom to joules per mole by using Avogadro's number.
		Formula/Rule: $Energy (J/mol) = Energy (J/atom) 	imes Avogadro's Number$
	3. Calculate the result
		Working:   $Energy (J/mol) = 13.6 	imes 1.602 	imes 10^{-19} 	imes 6.022 	imes 10^{23} = 1310135.104 \approx 1.31 	imes 10^6 $J/mol 
		Result: $1.31 	imes 10^6$ J/mol
		Verification: The calculated value matches with option C.
 ## OPTION ANALYSIS
[A] :x: Incorrect. This answer is too small by three orders of magnitude.
[B] :x: Incorrect. This answer is the energy in Joules per atom and not per mole and is also not the correct value.
[C] ✓: Correct. This matches the calculated result. 
[D] :x: Incorrect. The calculation is incorrect.
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Forgetting to multiply by Avogadro's number, resulting in energy per atom instead of per mole. [How to avoid]: Always remember to convert to per mole by multiplying with Avogadro's number.
		2.[Error 2]: Incorrect use of conversion factors. [How to avoid]: Always double-check the given conversion factors before using them.
	**Quick Tips**:
		1.[Helpful shortcut]: Break the problem into multiple steps: convert to Joules, then to per mole.
		2.[Memory aid]: Avogadro's number converts from per atom to per mole.

P.NARASIMHA · Answer

$1.31 	imes 10^3$ J/mol

P.NARASIMHA · Answer

$2.18 	imes 10^{-20}$ J/mol

P.NARASIMHA · Answer

The correct Option is "$1.31 	imes 10^6$ J/mol"

P.NARASIMHA · Answer

$8.21 	imes 10^5$ J/mol

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