Mass of 100 atoms of 14 7N is y × 10–22 in gm ,then value of y is (1 amu = 1.67 × 10–24 gm)

Key ideas and chain of thought

1. Atomic mass unit (amu)

   • By definition, $1\,\text{amu} = 1.67\times10^{-24}\,\text{g}$ (approx.).
   • Actual mass of an atom in grams = (mass in amu) $\times$ (conversion factor to grams).

2. Isotopic mass of $^{14}_{7}\text N$

   • For a light conceptual question we may take its mass number (14) to be its mass in amu.

   • Thus

     $m_{\text{one N-14 atom}} = 14\,\text{amu}$

3. Convert that to grams

   $m_{\text{one N-14 atom}} = 14\times1.67\times10^{-24}\,\text g$

4. Scale up to 100 atoms

   $m_{100\,\text{atoms}} = 100\times m_{\text{one atom}}$

5. Express in the demanded scientific form

   • After doing the multiplication you will have something like $2.338\times10^{-21}\,\text g$.
   • Convert it into the form $y\times10^{-22}$ by simply shifting the decimal place one step (that multiplies the mantissa by 10 and decreases the power by 1).

6. Read off $y$.

Imagine tiny marbles

1. One nitrogen marble (the isotope $^{14}_{7}\text N$) is said to weigh 14 tiny weight units called amu.
2. The question tells us 1 amu is the same as $1.67\times10^{-24}$ grams (super-duper light!).
3. First job: Find the weight of one nitrogen marble in grams.
4. Second job: Put 100 marbles together and see how heavy the whole bag is.
5. Finally, we must write that big‐number answer as $y\times10^{-22}$ grams and say what $y$ is.

So it is only multiplying two numbers (14 and 1.67) and then again by 100, and then shifting the decimal place so that the power of ten is $10^{-22}$.

Step-by-step calculation

1. Mass of one $^{14}_{7}\text N$ atom in grams

   m_{1} &= 14\,\text{amu}\times1.67\times10^{-24}\,\text{g/amu} \\ &= 23.38\times10^{-24}\,\text g \\ &= 2.338\times10^{-23}\,\text g \end{aligned}$$

2. Mass of 100 such atoms

   m_{100} &= 100\times m_{1} \\ &= 100\times2.338\times10^{-23}\,\text g \\ &= 2.338\times10^{-21}\,\text g \end{aligned}$$

3. Convert to the form $y\times10^{-22}$ g

   $2.338\times10^{-21}\,\text g = 23.38\times10^{-22}\,\text g$

4. Read off

   $y = 23.38 \;\approx 23.4$

Hence, the required value of $y$ is about 23.4 (often rounded to 23.4 or 23 depending on significant‐figure convention).