Question

The radius of a strontium atom is 215 pm. How many strontium atoms would have to be laid side by side to span a distance of 2.10 mm?

Answer 1

`4.883* 10^6 atoms` of strontium would be laid side by side to span a given distance.

Step-by-step explanation:

Radius of strontium atom ,r= 215 pm =
`2.15* 10^(-10) m`

`1 pm = 10^(-12) m`

Diameter of the strontium atom = d = 2r:

d =
`2* 2.15* 10^(-10) m=4.3* 10^(-10) m`[/tex]

let the number of strontium atoms be x

Length of the chain of strontium atoms laid side by side = 2.10 mm

1 mm = 0.001 m

=2.10 mm = 0.001 × 2.10 m =
`2.10* 10^(-3) m`

`x* d=2.10 mm`

`x* 4.3* 10^(-10) m=2.10* 10^(-3) m`

`x=(2.10* 10^(-3) m)/(4.3* 10^(-10) m)=4.883* 10^6 atoms`

`4.883* 10^6 atoms` of strontium would be laid side by side to span a given distance.

Answer 2

Here we have to get the number of strontium atom needed to be laid side by side to span a distance of 2.10 mm.

9.03×10⁷ number of strontium atoms are needed to cover the distance of 2.10mm.

The radius of the strontium atom is 215 pm, thus the diameter of strontium atom is (2×215) = 430 pm.

Now we know 1 pm is equivalent to 10⁻⁹ mm. Thus 430 pm is equivalent to (430×10⁻⁹) = 4.3×10⁻⁷ mm.

Thus 1 strontium atom can occupy 4.3×10⁻⁷mm of space. Now the distance to be occupied by the lay down of the strontium atom side by side of the span is 2.10 mm.

Hence,
`(2.10)/(4.3)`×10⁷ = 9.03×10⁷ number of atoms are needed.