Question

What mass of aluminum has a total nuclear charge of 2.9 c?

Answer 1

Complete Question

What mass of aluminum has a total nuclear charge of 2.9 C?

Aluminum has atomic number 13. Suppose the aluminum is all of the isotope with 14 neutrons.

Answer:

The mass is
`T_m  = 6.252 *10^(-5)\  g`

Step-by-step explanation:

From the question we are told that

The total nuclear charge is
`q =  2.9 \  C`

The atomic number is
`u  =  13`

The number of neutron is
`k  =  14`

Generally the number of positive charge is mathematically represented as

`N  = (q)/(p)`

here p is the charge on a single proton with value
`p =  1.60*10^(-19) \  C`

So

`N = (2.9)/(1.60*10^(-19))`

=>
`N = 1.813*10^(19) \ protons`

Now since 1 atom contains 13 proton

The number of atoms present is

`a =  (1.813*10^(19))/(13)`

`a =  1.395 *10^(18) \  atoms`

Then the number of moles present is mathematically represented as

`n = (a)/(N_k)`

Where N_k is the Boltzmann constant with value

`N_k  =  6.023*10^(23)`

So

`n  =  (1.395 *10^(18))/( 6.023*10^(23))`

`n = 2.315 *10^(-6)\  moles`

Generally one mole of aluminum is equal to 27 g

So

The total mass of aluminum is

`T_m  = n *  27`

=>
`T_m  = 2.315 *10^(-6)  *  27`

=>
`T_m  = 6.252 *10^(-5)\  g`