8. Show that the Bohr radius a0 = 4??0?² / mee² , indeed has the units of length. Recall the units: [?] = J · s, [?0] = N?¹m?²C² and [e] = C. Hint: Use F = ma and Ek = 1/2mv² to convert N and J to SI units.
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Step 1: Start with the given equation equating the electrostatic force to the centripetal force for a hydrogen atom: \[ \frac{e^2}{4\pi\epsilon_0 r^2} = \frac{mv^2}{r} \] Show more…
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- (a) Find the value of the Bohr radius $a_{\mathrm{B}}=\hbar^{2} /$ $\left(k e^{2} m\right)($ where $m$ is the electron's mass) by substituting the SI values of the constants concerned. (b) It is usually easier to do such calculations by using common combinations of constants, which can be memorized in convenient units $\left(k e^{2}=1.44 \mathrm{eV} \cdot \mathrm{nm}\right.$, for example). Find the value of the convenient combination $\hbar c$ in $\mathrm{eV} \cdot \mathrm{nm}$ from your knowledge of $h c$. [The value of $h c$ was given in equation $4.8 .$ Both $h c$ and $\hbar c$ are worth remembering in $\mathrm{eV} \cdot \mathrm{nm} .]$ Now calculate $a_{\mathrm{B}}$ by writing it as $(\hbar c)^{2} /\left(k e^{2} m c^{2}\right)$ and using known values of $\hbar c, k e^{2}$, and $m c^{2}$
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The Bohr Model of the Hydrogen Atom
The Bohr's radius is given by a0?=?me2?0?h2?. Verify that the RHS has dimensions of length.
Rajendra K.
Use the description of the Bohr atom given in the text to determine (a) the radius, in nanometers, of the sixth Bohr orbit for hydrogen; (b) the energy, in joules, of the electron when it is in this orbit.
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