 Solution

For a hot Jupiter transiting a Sun-sized star,a one-percent baseline transit. Taking $T\simeq 1500\mathrm{K}$, $g\simeq 20\mathrm{m}{\mathrm{s}}^{-2}$, and an ${\mathrm{H}}_2$-dominated mean molecular mass $\bar{m}\simeq 2.3m_H$ gives an atmospheric scale height near $270\mathrm{km}$. A strong band spanning five scale heights then hasor several hundred parts per million; very strong clear-atmosphere features can approach $10^{-3}$. The spectrum is therefore a roughly one-percent baseline with a localized Gaussian-sized band near ${\lambda }_0$ and a continuum rising toward short wavelengths when $\gamma <0$. Clouds reduce both $b$ and the observable power-law slope.

Solved by gpt-5.6-sol high.