近代物理

$\textrm{Photoelectri Effect}\\\begin{cases}E_{k_0}=h\nu -W_0=U_ce \\E_{k_1}=E_{k_0}+U_{正}e\\E_{光强}=nh\nu \\W_0=h\nu _c(截止频率) \end{cases}$ $\begin{cases} E_{pn}=-k\frac{e^2}{r_n} \\E_{kn}=k\frac{e^2}{2r_n} \end{cases}\Longrightarrow E_n=E_{pn}+E_{kn}=-k\frac{e^2}{2r_n}$ $\tilde{\nu}=\frac1\lambda=R(\frac{1}{2^2}-\frac{1}{n^2})\quad n=3,4,5,\cdots$ $E_n=\frac{1}{n^2}E_1\quad (E_1=-13.6\text{eV})\;\;r_n=n^2r_1$

$r=\frac{mv}{Bq}\\ m_\alpha v_\alpha=m_{Th}v_{Th}$ $\begin{cases} E=h\nu \\p=\frac{h}{\lambda}\end{cases} \triangle p\cdot\triangle x\ge\frac{h}{4\pi}$ $\rm\alpha 衰变\\ 2 _{1}^{1}H +2 _{0}^{1}n \rightarrow _{2}^{4}He \\ _{92}^{238}U \rightarrow_{90}^{234}Th +_{2}^{4}He\\\rm \beta衰变\\_{0}^{1}n \rightarrow _{1}^{1}H +_{-1}^{0}e\\ _{90}^{234}Th \rightarrow _{91}^{234}Pa + _{-1}^{0}e \\+\beta衰变\\_{1}^{1}H \rightarrow _{0}^{1}n +_{1}^{0}e\\ _{15}^{30}P \rightarrow _{14}^{30}Si + _{1}^{0}e$ $人工转变\\ \begin{cases}\rm _{2}^{4}He+ _{7}^{14}N \rightarrow _{8}^{17}O + _{1}^{1}H(Rutherford)\\\rm _{2}^{4}He+ _{4}^{8}Be \rightarrow _{6}^{11}C + _{0}^{1}n(Chadwick)\\\rm _{2}^{4}He+ _{13}^{27}Al \rightarrow _{15}^{30}P + _{0}^{1}n \\\rm _{15}^{30}P \rightarrow _{14}^{30}Si + _{1}^{0}e(I. Joliot-Curie) \end{cases}$