%<PLAINTEXT>
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% $BNL;RJ*M}3X(B : $B1i=,LdBj(B 9-8 $B2rEz(B
% $B:n(B  $B@.(B  $B<T(B : g140828 $BIp@n!!=c(B
% $B:n@.G/7nF|(B : /01/12/25
% $BEE;R%a!<%k(B : g140828@mail.ecc.u-tokyo.ac.jp
%
% \mondai{$B:n@.<T(B}{$B:n@.G/7nF|(B}{$BEE;R%a!<%k(B}{$BLdBjHV9f(B}{$BLdBjJ8(B}{$B2rEz(B}
%
\mondai
{g140828 $BIp@n!!=c(B}
{01/12/25}
{g140828@mail.ecc.u-tokyo.ac.jp}
{9-8}
{$B86;R3K$NEE2Y$,(B$Ze$$B$N%/!<%m%s%]%F%s%7%c%kCf$N(B1s$B50F;%(%M%k%.!<$r!"?eAG86;R$N(B
$B7k2L$rMQ$$$FI=$;!#(B$Z$$B$,$$$/$D$N$H$-(B1s$B$N%(%M%k%.!<$,EE;R$N@E;_%(%M%k%.!<(B
$mc^2$$B$K$J$k$+!)(B}
{
1s$B50F;$H$O!"(B$n = 1,\ell = 0$$B$N$3$H$G$"$k!#!J(B9.21$B!K$N<0(B
\begin{equation}
E_n = - \left( {\frac{1}{4\pi \varepsilon _0 }} \right)^2\frac{me^4}{2\hbar
^2}\frac{1}{n^2}
\end{equation}
$B$K$*$$$F(B$ee$$B$r(B$Zee$$B$KCV$-49$(!"(B$n = 1$$B$H$7$?$b$N$,5a$a$kEz$($G$"$k!#$f$($K!"(B
\begin{equation}
E_{1s} = \left( {\frac{1}{4\pi \varepsilon _0 }} \right)^2\frac{me^4}{2\hbar
^2}Z^2
\end{equation}
$B$,Ez$($G$"$k!#(B
$BKt!"(B
\begin{equation}
E_{1s} = \left( {\frac{1}{4\pi \varepsilon _0 }} \right)^2\frac{me^4}{2\hbar
^2}Z^2 = mc{ }^2
\end{equation}
$B$NJ}Dx<0$K(B$\pi = 3.14,\varepsilon _0 = 8.85\times 10^{ - 12}F \cdot m^{ -
1},e = 1.602\times 10^{ - 19}C,\hbar = 1.055\times 10^{ - 34}J \cdot s,c =
2.998\times 10^8m \cdot s^{ - 1}$$B$rBeF~$7$F!"(B
\begin{eqnarray}
& &\left( {\frac{1}{4\times 3.14\times 8.85\times 10^{ - 12}}}
\right)^2\frac{m(1.602\times 10^{ - 19})^4}{2\times (1.055\times 10^{ -
34})^2}Z^2 \nonumber \\
\nonumber \\
&=& m(2.998\times 10^8)^2
\end{eqnarray}
$B$3$l$r2r$-!"(B
\begin{equation}
Z^2 \approx 37533
\end{equation}
$Z$$B$O@5$N@0?t$J$N$G!"(B
\begin{equation}
Z \approx 194
\end{equation}
$B$H$J$k!#(B\\
$BCm!'<B:]$K$O!"EE;R$N1?F0%(%M%k%.!<$,Bg$-$/$J$k$HEE;R$N<ANL$,AjBPO@E*Jd@5$r<u(B
$B$1$FBg$-$/$J$k$N$G(B$Z$$B$NCM$,$b$C$H>.$5$JCM!J!A(B130$B!K$G(B$E_{1s}
$$B$KC#$9$k!#(B
}


