Question

The radius of hydrogen atom is 0.43 ×10¹² m convert it in cm,mm,nm

Answer 1

Answer on Question #79533- Physics - Atomic and Nuclear Physics

Question: The radius of hydrogen atom is $0.43 \times 10^{12} \, \text{m}$ convert it in cm, mm, nm

Answer:

First of all, one should note that the given number (pay attention to the power) is extremely large: it is almost three times the distance between the Sun and the Earth. Obviously, there is a typos here, however, switching to power -12 also does not lead to the right result.

According to [1], the radius of a hydrogen atom is about $0.53 \times 10^{-10} \, \text{m}$ (it is called Bohr radius). In order to calculate this value in cm, mm and nm, one should recall that $1 \, \text{cm} = 10^{-2} \, \text{m}$; $1 \, \text{mm} = 10^{-3} \, \text{m}$; $1 \, \text{nm} = 10^{-9} \, \text{m}$. Hence,

$$\begin{array}{l} 0.53 \cdot 10^{-10} \, \text{m} = 0.53 \cdot \frac{10^{-10}}{10^{-2}} \, \text{cm} = 0.53 \cdot 10^{-8} \, \text{cm} \\ = 0.53 \cdot \frac{10^{-10}}{10^{-3}} \, \text{mm} = 0.53 \cdot 10^{-7} \, \text{mm} \\ = 0.53 \cdot \frac{10^{-10}}{10^{-9}} \, \text{nm} = 0.53 \cdot 10^{-1} \, \text{nm} \end{array}$$

In case if it was necessary to consider the given number, there is also an answer as follows:

$$0.43 \cdot 10^{12} \, \text{m} = 0.43 \cdot 10^{14} \, \text{cm} = 0.43 \cdot 10^{15} \, \text{mm} = 0.43 \cdot 10^{21} \, \text{nm}$$

[1] (Electronic resource) https://en.wikipedia.org/wiki/Hydrogen_atom

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