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In the ground state of hydrogen, according to the Bohr model, an electron orbits 5.3 x 10-11 m from the nucleus. It undergoes a centripetal acceleration of 9.0 x 1022 m/s2.
a) Find its speed.
b) In an excited state with principle quantum number n = 10, the electron is 100 times farther away, and its centripetal acceleration is 10,000 times.

Respuesta :

Answer:

Explanation:

Given

radius of electron[tex](r)=5.3\times 10^{-11} m[/tex]

centripetal acceleration [tex](a_c)=9\times 10^22 m/s^2[/tex]

we know

[tex]a_c=\frac{v^2}{r}[/tex]

[tex]v=\sqrt{r\times a_c}[/tex]

[tex]v=\sqrt{5.3\times 10^{-11}\times 9\times 10^{22}}[/tex]

[tex]v=\sqrt{47.7\times 10^11}[/tex]

[tex]v=21.84\times 10^5 m/s[/tex]

(b)For n=10

[tex]r=100\times 5.3\times 10^{-11} m\approx 5.3\times 10^{-9} m[/tex]

[tex]a_c=10^4\times 9\times 10^{22} m/s^2[/tex]

[tex]a_c=9\times 10^{26} m/s^2[/tex]

[tex]v=\sqrt{r\times a_c}[/tex]

[tex]v=\sqrt{9\times 10^{26}\times 5.3\times 10^{-9}}[/tex]

[tex]v=21.84\times 10^8 m/s[/tex]

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