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3 years ago

If the sun is scaled down to 9.5 inches in diameter, the earth would be about _____ inches in diameter

Physics

1 answer:

vovangra [49]3 years ago

7 0

Answer: 0.087 inches

Explanation:

This problem can be solved applying the Rule of three, which is a mathematical rule to find out an amount that is with another quantity given in the same relation as other two also known.

In this sense, the actual diameter of the Sun is 1,391,020 km and the actual diameter of the Earth is 12,742 km.

Now, applying the Rule of three:

Sun 1,391,020 km ------ 9.5 inches

Earth 12,742 km --------- ? inches

$? inches=\frac{(12,742 km)(9.5 inches)}{1,391,020 km}$

$? inches=0.087 inches$

Therefore:

If the sun is scaled down to 9.5 inches in diameter, the earth would be about 0.087 inches in diameter.

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Explanation:

They give us some spectral lines of the Balmer series, let's take the opportunity to place the values in SI units

n = 3 λ = 656.3 nm = 656.3 10⁻⁹ m

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Let's use the Planck equation

E = h f

The speed of light equation

c = λ f

replace

E = h c /λ

Where h is the Planck constant that is worth 6.63 10⁻³⁴ J s and c is the speed of light that is worth 3 10⁸ m / s

Let's calculate the energies

E = 6.63 10⁻³⁴ 3 10⁸ / λ

E = 19.89 10⁻²⁶ /λ

n = 3

E3 = 19.89 10⁻²⁶ / 656.3 10⁻⁹

E3 = 3.03 10⁻¹⁹ J

1 kJ = 10³ J

E3 = 3.03 10⁻¹⁶ kJ

n = 4

E4 = 19.89 10⁻²⁶ /486.1 10⁻⁹

E4 = 4.09 10⁻¹⁹ J

E4 = 4.09 10⁻¹⁶ kJ

n = 5

E5 = 19.89 10⁻²⁶ /434.0 10⁻⁹

E5 = 4.58 10⁻¹⁹ J

E5 = 4.58 10⁻¹⁶ kJ

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3 years ago