Question

Find (a) the total number and (b) the total mass of neutrons in 7 mg of 14C. (Assume that mass of a neutron = 1.675 × 10^–27 kg).​

Answer 1

Answer:

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Mass of one neutron

= 1.675 × 10^–27 kg

1 mole of Carbon atom

= 6.023×10²³ atoms

Number of neutrons in 1 carbon atom

= 14-6= 8

So total number of neutrons in 14g of Carbon

= 6.023×10²³×8 neutrons

So 7mg of Carbon will contain

= 6.023 x 10²³ x 8 x 7 x 10^-3 / 14

= [3.37288×10²²]/14

= 2.4092×10²¹ neutrons

So, Mass of 2.4092×1021 neutrons

= [2.4092×10²¹] × [1.675 × 10^–24]

= 4.035×10^–3 g

So, in 7 mg of carbon total number of neutrons is 2.41×10²¹ and the total mass of the neutrons is 4.035× 10^–3 g

Answer 2

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number of electrons in 14c=6

therefore number of protons=14-6=8

now....

we know ....1g=1000mg

now mass of 14C= 14g=14×1000mg

will have =(8×6.023×10²³ )numbers of neutrons

therefore ....

in 7mg... number of neutrons is ....

=

$\frac{8 \times 6.023 \times 10 {}^{23} }{14000} \times 7 \\ = 2.4092 \times 10 {}^{21}$

mass of a single neutron is =1.675×10^-27kg

therefore mass of 2.4092×10^21 number of neutrons is

$= 1.675 \times 10 {}^{ - 27} \times 2.4092 \times 10 {}^{21} \\ = 4.035 \times 10 {}^{ - 6} kg$