Question

How many coulombs of positive charge (in units of 107 C) are there 1.53 kg of plutonium, given its atomic mass is 244 and that each plutonium atom has 94 protons? 1 atomic mass unit = 1.66*10-27 kg Enter a number with two digits behind the decimal point.

Answer 1

The value is
`q =  5.72 *10^7 \  C`

Step-by-step explanation:

From the question we are told that

the mass is
`m  =  1.53 \ kg`

The atomic mass is
`u  =  244 g/mol =  0.244 kg/mol`

The number of protons on each atom is
`N  =  94 \  protons`

The mass of one atomic mass unit is
`M  = 1.66 *10^(-27) \  kg`

Generally the number of atoms present is

`k  =  (m *  N_a )/(u)`

Here
`N_a` is the Avogadro constant with value
`N_a  =  6.023  *10^(23) \  atoms /mol`

=>
`k  =  (1.53 * 6.023*10^(23))/( 0.244)`

=>
`k  =  3.8 *10^(24) \  atoms`

The coulombs of positive charge on the plutonium is mathematically represented as

`q =  k *  N  *  e`

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

`q = 3.8 *10^(24) *  94 *  1.60*10^(-19)`

`q =  5.72 *10^7 \  C`