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Question: The atomic weight of a hydrogen atom is: A. \(1.76\times {{10}^{-27}}kg\) B. \(1.73\times {{10}^...

The atomic weight of a hydrogen atom is:
A. 1.76×10−27kg1.76\times {{10}^{-27}}kg
B. 1.73×10−27kg1.73\times {{10}^{-27}}kg
C. 1.66×10−27kg1.66\times {{10}^{-27}}kg
D. None of these

Explanation

Solution

Hint: Remember that the atomic or molecular mass of a molecule of a given substance is given by its gram-atomic mass by the Avogadro number which is 6.022×10236.022\times {{10}^{23}}. Use this relationship between the two to try and solve this question.

Complete step by step solution:
Let us first clear up what the definition of atomic and gram-atomic mass really is before applying said concept to obtain the answer to this question.
The atomic mass of an element is the average mass of the atoms of an element measured in atomic mass unit. The atomic mass is a weighted average of all of the isotopes of that element, in which the mass of each isotope is multiplied by the abundance of that particular isotope.
The gram atomic mass (weight) of an element is the mass of Avogadro number (6.022×1023)(6.022\times {{10}^{23}}) of atoms of that elements in grams. For example,
Mass of 1 atom of oxygen = 16 amu
Mass of 1 mole of oxygen = 16 gm
Mass of atoms of oxygen= 166.022×1023×6.022×1023\dfrac{16}{6.022\times {{10}^{23}}}\times 6.022\times {{10}^{23}} = 16 gm.
Hence, Gram atomic weight of oxygen = 16 gm.
Also, it is worth noting that:
No. of gram atoms = mass of element in gmatomic mass of element in gm No.\text{ }of\text{ }gram\text{ }atoms\text{ }=\text{ }\dfrac{mass\text{ }of\text{ }element\text{ }in\text{ }gm}{atomic\text{ }mass\text{ }of\text{ }element\text{ }in\text{ }gm}\text{ }
Now, let us apply these concepts to help find the solution to the given question.
Gram-atomic mass of Hydrogen = 1 g
Atomic mass of Hydrogen = 16.022×1023g\dfrac{1}{6.022\times {{10}^{23}}}g = 1.66×10−27kg1.66\times {{10}^{-27}}kg
Therefore, the answer to this question is ‘C. 1.66×10−27kg1.66\times {{10}^{-27}}kg’

Note:
Remember that there is a stark difference between the atomic and gram-atomic masses of a substance, both of which are distinctly different from its molecular and molar mass. Be very careful of this distinction when trying to solve this question.