Question

CO\(_2\) concentration in the Earth's atmosphere is increasing because 50% of the annual anthropogenic emissions are retained in the atmosphere. If nations agree to reduce annual CO\(_2\) emissions by one Giga ton every year starting from 2021, then in which year will the CO\(_2\) concentration in the atmosphere stop rising due to anthropogenic emissions? Take the anthropogenic CO\(_2\) emissions in 2020 as 40 Giga tons.

• A. 2020
• B. 2050
• C. 2060
• D. 2100

Hint:

When considering the effects of emissions over time, remember that the reduction in emissions will slow the rate of increase in atmospheric CO\(_2\), but it may take decades for emissions to stabilize fully.

Answer 1

The Correct Option is C

We are given that 50% of the annual anthropogenic emissions are retained in the atmosphere, and emissions are reduced by 1 Giga ton every year starting from 2021. The total emissions in the atmosphere depend on the emissions in each year and how much of it stays in the atmosphere.

Step 1: Initial Conditions and Rate of Reduction
In 2020, the emissions are 40 Giga tons, and 50% of this is retained in the atmosphere. Thus, the amount of CO\(_2\) that stays in the atmosphere from the emissions in 2020 is: \[ 40 \times 0.5 = 20 \, \text{Giga tons}. \] In 2021, the emissions are reduced to 39 Giga tons, and 50% of this is retained in the atmosphere: \[ 39 \times 0.5 = 19.5 \, \text{Giga tons}. \] Similarly, in 2022, the emissions are reduced to 38 Giga tons, and half of this is retained: \[ 38 \times 0.5 = 19 \, \text{Giga tons}. \]

Step 2: Cumulative Effect of Emissions
The amount of CO\(_2\) in the atmosphere increases each year by the retained emissions. If the emissions continue to decrease by 1 Giga ton each year starting from 2021, the accumulated emissions from all the years will continue to contribute to the increase in CO\(_2\) concentration in the atmosphere. The total retained emissions can be calculated cumulatively: \[ \text{Total retained emissions} = 20 + 19.5 + 19 + \dots. \] Since emissions are being reduced each year, it will take time for the contributions to reduce sufficiently for the total emissions to stop rising. In this case, by the year 2060, the emissions will have reduced enough that the total amount of CO\(_2\) in the atmosphere due to anthropogenic emissions will stop rising, assuming that all emissions are retained. Thus, the year when the CO\(_2\) concentration in the atmosphere stops rising due to anthropogenic emissions is around 2060.

Final Answer: \[ \boxed{2060}. \]