SME
Historical Geology · Problem type
Age from an isochron
Use this for “Samples of one granite plot on a line of slope 0.0145 on a graph of ⁸⁷Sr/⁸⁶Sr against ⁸⁷Rb/⁸⁶Sr. How old is the granite?”
Chart
y-intercept (0, 0.7045)
y(2) = 0.7335
This is an example. Type your own values to start a new problem.
t (Ma)
=
ln(1
+
m
)
÷
λ (yr⁻¹)
(⁸⁷Sr/⁸⁶Sr)₀
Initial ratio
example
x
A sample’s ⁸⁷Rb/⁸⁶Sr
example
y
That sample’s ⁸⁷Sr/⁸⁶Sr
calculated
Formulas
m
=
e
λ
×
t
−
1
0.0145
=
e
1.42 ×
10
-11
× (1.0138 ×
10
9
)
−
1
y
=
(⁸⁷Sr/⁸⁶Sr)₀
+
m
×
x
0.7335 = 0.7045 + 0.0145 × 2
Formulas are worked in yr. The step-by-step shows the conversions.
Assumptions
•
The samples formed together from one melt, so all began with the same ⁸⁷Sr/⁸⁶Sr: the initial ratio, where the line meets the axis.
•
Rb-87 decays to Sr-87 with λ = 1.42 × 10⁻¹¹ per year, so each point climbs by its ⁸⁷Rb/⁸⁶Sr times eλt − 1: the slope.
•
The slope grows with age alone, so no starting daughter needs guessing; the rock stayed closed since it formed.
Step-by-step
WE KNOW
m = 0.0145, λ = 1.42 × 10⁻¹¹ yr⁻¹, (⁸⁷Sr/⁸⁶Sr)₀ = 0.7045, x = 2
FIND
age (t), that sample’s ⁸⁷Sr/⁸⁶Sr (y)
Step 1 · Find age (t)
Use m = eλ × t − 1
Add 1 to the slope, take ln to undo the e, then divide by the decay constant.
t
=
ln(1 +
m
)
λ
t
=
ln(1 + 0.0145)
1.42 ×
10
-11
ln(1 + 0.0145) = 0.0144
t
=
1.0138 ×
10
9
yr
Step 2 · Find that sample’s ⁸⁷Sr/⁸⁶Sr (y)
Use y = (⁸⁷Sr/⁸⁶Sr)₀ + m × x
The sample started at the initial ratio and gained slope × ⁸⁷Rb/⁸⁶Sr of new Sr-87.
y
=
0.7045
+
0.0145
×
2
y
=
0.7045
+
0.029
y
=
0.7335
Step 3 · Convert the answers
Change each answer back to the unit you chose.
t = 1.0138 × 10⁹ yr = 1,014 Ma (1 Ma = 10⁶ yr)
Check
Put the numbers back in. Both sides should match.
0.0145
=
e
1.42 ×
10
-11
× (1.0138 ×
10
9
)
−
1
✓
0.7335 = 0.7045 + 0.0145 × 2 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Radiometric dating
Main lesson
Potassium–argon age with the branching decay
Use this for “A lava flow holds 0.01 argon-40 atom for every potassium-40 atom. How long ago did it cool?”
Radiocarbon age from activity
Use this for “Charcoal from a hearth gives 3.4 decays per minute per gram, and living carbon gives 13.6. How old is the charcoal?”