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

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What mass of aluminum has a total nuclear charge of

Ответ:

jaztbrown374

01.02.2022

Physics

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.

The mass is $T_m = 6.252 *10^{-5}\ g$

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

$N = \frac{q}{p}$

here p is the charge on a single proton with value $p = 1.60*10^{-19} \ C$

$N = \frac{2.9}{1.60*10^{-19}}$

=> $N = 1.813*10^{19} \ protons$

Now since 1 atom contains 13 proton

The number of atoms present is

$a = \frac{1.813*10^{19}}{13}$

$a = 1.395 *10^{18} \ atoms$

Then the number of moles present is mathematically represented as

$n = \frac{a}{N_k}$

Where N_k is the Boltzmann constant with value

$N_k = 6.023*10^{23}$

$n = \frac{1.395 *10^{18}}{ 6.023*10^{23}}$

$n = 2.315 *10^{-6}\ moles$

Generally one mole of aluminum is equal to 27 g

The total mass of aluminum is

T_m = n * 27

=> $T_m = 2.315 *10^{-6} * 27$

=> $T_m = 6.252 *10^{-5}\ g$

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

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