Question

Nitu presented a silver lamp to her mother on her birthday. The lamp contains 3.011*10 raised to power 24 atoms of silver in it. What is the mass of the lamp and the cost of it, if 1 gram of silver costs rupees 60.23 ? (Atomic mass of Ag=108u).
Solve using unitary method.

Answer 1

Answer:-

• Mass of the lamp = 540g

• Cost of it = ₹ 32524.20

Explanation:-

It is given that the lamp presented by Nitu to her mother contained 3.011×10²⁴ atoms of silver in it.

→ Atomic mass of silver = 108u

→ Cost of 1g Silver = ₹ 60.23

→ Avovadro Number = 6.022×10²³

Since, atomic mass of silver is 108u, thus it's molar mass is 108g/mol.

Firstly, let's calculate the number of moles in 3.011×10²³ atoms of silver.

No of moles :-

= No of particles/Avogadro Number

= 3.011×10²⁴/6.022×10²³

= 0.5×10

= 5 moles

Mass = No of moles × Molar mass

=> Mass = 5×108

=> Mass = 540g

Now, cost of the lamp:-

= 540×60.23

= ₹ 32524.20

Thus:-

• Mass of the lamp is 540g.

• Cost of it is ₹ 32524.20

Answer 2

We have,

Number of Ag atoms in the lamp = 3.011 × 10²³

Rate = Ru. 60.23 per 1 g of Ag

Atomic mass of Ag = 108 u

We know,

Number of moles = (Number of atoms)/(N_A)

⇒ No. of moles = (3.011 × 10²⁴)/(6.022 × 10²³)

⇒ No. of moles = ½ × 10

⇒ No. of moles = 5 mol

Now we know,

Given mass = Number of moles × Molar mass

⇒ Given mass = 5 × 108 g

⇒ Given mass = 540 g ...(I)

∴ Cost of the lamp = Mass × Rate = 540 g × Ru. 60.23/g

⇒ Cost = 54 × 602.3

⇒ Cost = 32524.2 ...(II)