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Home » First, convert each mixed number to an improper fraction: - Network4

First, convert each mixed number to an improper fraction: - Network4

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 A theoretical physicist demonstrates energy levels in a quantum model where the energy of a particle in the nth state is $ E_n = -13.6/n^2 $ eV. What is the energy difference between the n=2 and n=3 states?

📌 For $ n=2 $: $ E_2 = -13.6 / 2^2 = -13.6 / 4 = -3.4 $ eV.

📌 For $ n=3 $: $ E_3 = -13.6 / 3^2 = -13.6 / 9 \approx -1.511 $ eV.

📌 The energy difference is $ \Delta E = E_2 - E_3 = -3.4 - (-1.511) = -3.4 + 1.511 = -1.889 $ eV.

📌 The magnitude of the energy difference is 1.889 eV.

📌 A science communicator explains radioactive decay using a sample with a half-life of 8 years. If the initial mass is 200 grams, how much remains after 24 years?

📌 Number of half-lives: $ 24 / 8 = 3 $.

📌 Remaining mass = $ 200 \times (1/2)^3 = 200 \times 1/8 = 25 $ grams.

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Bessere Zahlen:
\( \frac{8}{3} \), \( (\frac{8}{3})^2 = \frac{64}{9} \), \( (\frac{8}{...
Jede Term:
\( (z + \frac{8}{3})^3 = z^3 + 3\cdot\frac{8}{3}z^2 + 3\cdot\frac{64}{...
\( -8(z + \frac{8}{3})^2 = -8(z^2 + \frac{16}{3}z + \frac{64}{9}) = -8...
\( 9(z + \frac{8}{3}) = 9z + 24 \)
Summe:
z^3 + 8z^2 + \frac{64}{3}z + \frac{512}{27} -8z^2 - \frac{128}{3}z - \...
= z^3 + \left(8 - 8\right)z^2 + \left(\frac{64 - 128 + 27}{3}\right)z...
= z^3 + \left(\frac{-407}{3}\right)z + \left(\frac{512 - 1536 + 648 -...

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