PHY232 Homework Sheet 2 DEPARTMENT OF PHYSICS … · PHY232 Homework Sheet 2 DEPARTMENT OF PHYSICS...
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PHY232 Homework Sheet 2 DEPARTMENT OF PHYSICS AND ASTRONOMY PHY232: The Dynamic Interstellar Medium Homework Sheet No.2 Deadline: Friday 30 Apr 2010: General Office E34 1. The transition frequency between quantum numbers n and m of atomic hy- drogen is: ν n,m = R 1 n 2 - 1 m 2 , where R =3.3 × 10 15 Hz. In which part of the electromagnetic spectrum does the line transition between the n=110 and n=111 orbitals occur? [10] 2. (a) Derive the equation for the Str¨omgren radius, R s of a dust-free, pure hydrogen gaseous nebula, R 3 s = 3 4π Q 0 n 2 β B , where Q 0 is the rate at which the star emits Lyman continuum pho- tons, n is the number density of hydrogen nuclei and β B is the Case B recombination coefficient. [15] (b) Calculate R s in parsec for the case of an O star with Q 0 = 10 48.8 pho- ton s -1 , with density n =5 × 10 9 m -3 and temperature T e = 9,000 K. [10] (c) What effect does the presence of dust within a HII region have upon R s ? Explain why this is so. [10] 3. Qualitatively compare the nature of the ionizing radiation in HII regions and planetary nebulae. How are dynamical ages of planetary nebulae derived? [20] 4. (a) In a HII region the electron temperature may be derived from Δλ, the full-width at half-maximum (FWHM) of a nebular line, at a wavelength λ via Δλ λ = 2 c ln 2 1/2 2kT e m + v 2 turb ! 1/2 where v turb is due to the bulk motion of the gas. Derive T e if Δλ=0.04 nm for Hβ (486.1 nm) and Δλ=0.029 nm for [OIII] 500.7 nm. [25] (b) Would you expect this HII region to be located within the metal-rich inner Milky Way or metal-poor outer disk? Justify your answer. [10]
Transcript of PHY232 Homework Sheet 2 DEPARTMENT OF PHYSICS … · PHY232 Homework Sheet 2 DEPARTMENT OF PHYSICS...
PHY232 Homework Sheet 2
DEPARTMENT OF PHYSICS AND ASTRONOMY
PHY232: The Dynamic Interstellar Medium
Homework Sheet No.2
Deadline: Friday 30 Apr 2010: General Office E34
1. The transition frequency between quantum numbers n and m of atomic hy-drogen is:
νn,m = R(
1
n2− 1
m2
),
where R = 3.3× 1015 Hz. In which part of the electromagnetic spectrum doesthe line transition between the n=110 and n=111 orbitals occur? [10]
2. (a) Derive the equation for the Stromgren radius, Rs of a dust-free, purehydrogen gaseous nebula,
R3s =
3
4π
Q0
n2βB
,
where Q0 is the rate at which the star emits Lyman continuum pho-tons, n is the number density of hydrogen nuclei and βB is the Case Brecombination coefficient. [15]
(b) Calculate Rs in parsec for the case of an O star with Q0 = 1048.8 pho-ton s−1, with density n = 5 × 109 m−3 and temperature Te = 9,000 K. [10]
(c) What effect does the presence of dust within a HII region have upon Rs?Explain why this is so. [10]
3. Qualitatively compare the nature of the ionizing radiation in HII regions andplanetary nebulae. How are dynamical ages of planetary nebulae derived? [20]
4. (a) In a HII region the electron temperature may be derived from ∆λ, thefull-width at half-maximum (FWHM) of a nebular line, at a wavelengthλ via
∆λ
λ=
2
cln 21/2
(2kTe
m+ v2
turb
)1/2
where vturb is due to the bulk motion of the gas. Derive Te if ∆λ=0.04 nmfor Hβ (486.1 nm) and ∆λ=0.029 nm for [OIII] 500.7 nm. [25]
(b) Would you expect this HII region to be located within the metal-richinner Milky Way or metal-poor outer disk? Justify your answer. [10]
