Question

The mass of an atom of sodium is 23 u. Calculate the
number of sodium atoms in 1 mg.
Take 1 u = 1.66 x 10^-27 kg.

the answer is 2.62×10^19
I need the process , to solve it​

Answer 1

Answer :-

2.62 × 10¹⁹ atoms are there in 1 mg.

Explanation :-

We have :-

→ Mass of a sodium atom = 23 u

→ Given mass = 1 mg

→ 1 u = 1.66 × 10⁻²⁷ kg

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We know that :-

• 1 kg = 10⁶ mg

Firstly, let's convert the mass of the Sodium atom from unified mass (u) to miligram (mg).

⇒ 1 u = (1.66 × 10⁻²⁷ × 10⁶) mg

⇒ 1 u = 1.66 × 10⁻²⁷⁺⁶

⇒ 1 u = 1.66 × 10⁻²¹ mg

⇒ 23 u = 23 × 1.66 × 10⁻²¹ mg

⇒ 23 u = 38.18 × 10⁻²¹ mg

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Now, required number of Sodium atoms will be :-

= Given Mass/Mass of 1 atom (mg)

= 1/(38.18 × 10⁻²¹)

= 1/38.18 × 1/10⁻²¹

= 0.0262 × 10²¹

= 2.62 × 10¹⁹ atoms

Answer 2

Answer:

Given :-

• The mass of an atom of sodium is 23u.
• 1u = 1.66 × 10-²⁷ kg.

To Find :-

• What is the number of sodium atoms in 1 mg.

Solution :-

First, we have to convert u to mg :

$\implies \sf Sodium\: of\: 1\: atom =\: 23u$

We have :

$\leadsto \sf\bold{1u =\: 1.66 \times 10^{- 27}}\: kg$

$\implies \sf Sodium\: of\: 1\: atom =\: 23(1.66 \times 10^{- 27})\: kg$

$\implies \sf Sodium\: of\: 1\: atom =\: 23 \times 1.66 \times 10^{- 27}\: kg$

$\implies \sf Sodium\: of\: 1\: atom =\: 23 \times \dfrac{166}{100} \times 10^{- 27}\: kg$

$\implies \sf Sodium\: of\: 1\: atom =\: \dfrac{3818}{100} \times 10^{- 27}\: kg$

$\implies \sf Sodium\: of\: 1\: atom =\: 38.18 \times 10^{- 27}\: kg$

$\implies \sf Sodium\: of\: 1\: atom =\: 38.18 \times 10^{- 27} \times 10^6\: mg\: \bigg\lgroup \sf\bold{1\: kg =\: 10^6\: mg}\bigg\rgroup$

$\implies \sf Sodium\: of\: 1\: atom =\: 38.18 \times 10^{(- 27 + 6)}\: mg$

$\implies \sf\bold{\purple{Sodium\: of\: 1\: atom =\: 38.18 \times 10^{- 21}\: mg}}$

Now, we have to find the number of sodium atoms in 1 mg :

As we know that,

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Number\: of\: Sodium\: atoms =\: \dfrac{Mass}{Mass\: of\: 1\: atom\: (mg)}}}}$

Given :

$\bigstar\: \: \rm{\bold{Mass =\: 1\: mg}}$

$\bigstar\: \: \rm{\bold{Mass\: of\: 1\: atom\: (mg) =\: 38.18 \times 10^{- 21}\: mg}}$

According to the question by using the formula we get,

$\longrightarrow \sf Number\: of\: Sodium\: atoms =\: \dfrac{1}{38.18 \times 10^{- 21}}$

$\longrightarrow \sf\bold{\red{Number\: of\: Sodium\: atoms =\: 2.62\: \times 10^{19}\: atoms}}$

$\therefore$ The number of sodium atoms is 2.62 × 10¹⁹.