Question

What is the charge on 1.0 kg of protons? (e = 1.60 × 10-19 c, mproton = 1.67 × 10-27 kg)?

Answer 1

First, we need to find the number of protons, which is the total mass divided by the mass of one proton:
$N= \frac{m}{m_p}= \frac{1.0 kg}{1.67 \cdot 10^{-27} kg}=6.0 \cdot 10^{26}$ protons

Then, the total charge is the number of protons times the charge of a  single proton:
$Q=Ne = 6.0 \cdot 10^{26}\cdot 1.60 \cdot 10^{-19} C=9.6 \cdot 10^7 C$

Answer 2

9.6 x 10⁷ C.

Further explanation

Given:

• The total mass of protons = 1.0 kg
• The mass of one proton = $1.67 \times 10^{-27} \ kg$
• The elementary charge of proton = $1.602 \times 10^{-19} \ C$

Question:

What is the charge on 1.0 kg of protons?

The Process:

Atoms consist of smaller or subatomic particles, namely protons (p), electrons (e), and neutrons (n).

• Protons are positively charged subatomic particles.
• Electrons are negatively charged subatomic particles.
• Neutrons are subatomic particles with no charge.

Step-1: find the number of protons

$\boxed{ \ N = \frac{total \ mass}{mass \ of \ one \ proton} \ }$

$\boxed{ \ N = \frac{1.0 \ kg}{1.67 \times 10^{-27} \ kg} \ }$

Hence, $\boxed{ \ N = 5.99 \times 10^{26} \ protons} \ }$

Step-2: find the charge

By using this formula,

$\boxed{ \ Q = Ne \ }$

we calculate the total charge of the protons.

Recall $e = 1.602 \times 10^{-19} \ C$

$\boxed{ \ Q = (5.99 \times 10^{26})(1.602 \times 10^{-19}) \ }$

Thus, the charge on 1.0 kg of protons is $\boxed{\boxed{ \ 9.6 \times 10^7 \ C \ }}$

Quick Steps

$\boxed{ \ Q = 1.0 \ kg \times \frac{1 \ proton}{1.67 \times 10^{-27} \ kg} \times \frac{1.60 \times 10^{-19} \ C}{1 \ proton} \ } \rightarrow \boxed{ \ Q = 9.6 \times 10^7 \ C \ }$

Learn more

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Keywords: the charge, protons, the mass, the number, elementary